
Personal:
US citizen, born May 19, 1957, in Sofia, Bulgaria, wife Irina Sousokolova, son Boyan and daughter Anna
University Education:
Research and Teaching Positions:
19821983 
Research Assistant, Institute of Mathematics Bulgarian Academy of Sciences, Sofia

MayJune 1986

Visiting Professor at Institute Fourier, Grenoble, France

19871989  Research Fellow, Section of Algebra, Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria

Oct. 1989  Visiting Professor at the University of Paris VII, France

Jan.Dec. 1990  Visiting Assistant Professor, Department of Mathematics, University of California at Berkeley

JuneJuly 1990  Visiting Scholar at the University of Göttingen, Germany

Jan.June 1991  Visiting Assistant Professor, Department of Mathematics, University of California at Davis

1991June 93  Assistant Professor, Department of Mathematics, University of California at Riverside

Sept. Oct. 1993  Visiting Scholar at the Erwin Schrödinger Institute, Vienna, Austria

July 1993June 00  Associate Professor (tenured appointment), Department of 
Mathematics, University of California at Riverside
 
Apr.–May 1996  Visiting Scholar and Program Organizer at The Erwin Schrödinger Institute, Vienna, Austria

June 1996  Visiting Scholar at the MaxPlanck Institute of Mathematics, Bonn, Germany June

1997  Visiting Professor at the University of Burgundy Dijon, France

Sept. 1997  Visiting Professor at the University Louis Pasteur, Strasbourg, France

Aug.Sept. 1998  Visiting Scholar at the MaxPlanck Institute of Mathematics, Bonn, Germany

Nov. 1999  Visiting Professor at the University of Hamburg, Germany

AprilJune 2000 
Visiting Scholar at the MaxPlanck Institute of Mathematics, Bonn, Germany

July 2000  Oct 04  Professor (tenured appointment), Department of Mathematics, University of California at Riverside

Aug.Sept. 2001  Visiting Scholar at the MaxPlanck Institute of Mathematics, Bonn, Germany

Jan.March 2002  Program organizer and MSRI scholar, MSRI, Berkeley

Aug.Sept. 2002  Visiting Scholar at the MaxPlanck Institute of Mathematics, Bonn, Germany

Fall 2003  Visiting Professor at Yale University

Spring 2004  Visiting Scholar at the MaxPlanck Institute of Mathematics, Bonn, Germany

Fall 2007  Visiting Professor at University of California at Berkeley 
Spring 2012  Visiting Professor at Yale University 
Fall 2012  Visiting Scholar at the MaxPlanck Institute of Mathematics, Bonn, Germany

Since 2004  Professor, Jacobs University Bremen, Germany

Main Research Interests:
Representations of finite and infinite dimensional Lie algebras, generalized HarishChandra modules, representations of Lie superalgebras and Lie supergroups, geometry of supermanifolds, homogeneous superspaces, super Dmodules, homogeneous indspaces and geometry of indvarieties.
19911995  NSF research grant jointly with R.E.Block and V.Chari. 
1995  NSF grant for organizing the conference in honor of R.E.Block (jointly with V.Chari). 
1995  Grant from the Erwin Schr\"odinger Institute for the program ``Representation Theory with Applications to Mathematical Physics'' (jointly with Joseph A. Wolf). 
1996  NSF grant for support of US graduate students at the Erwin Schr\"odinger Institute. 
19951997  NSF research grant. 
19972002  NSF Group Infrastructure Grant ``Lie Groups, Lie Algebras and Their Representations'' (jointly with Joseph A. Wolf and Geoffrey Mason). 
JanMay, 2002  Coorganizer of the onesemester MSRI Program ``Representations of Infinite Dimensional Algebras and Mathematical Physics'' (jointly with Edward Frenkel, Victor Kac, Vera Serganova and Gregg Zuckerman). 
April 2002  Coorganizer of the MSRI Workshop ``Quantum field theory and supersymmetry''. 
Sept. 2003  Coorganizer of the workshop ``Locally finite Lie algebras'' at the Banff Research Institute, Canada. 
20032006  NSF Grant ``Lie Groups, Lie Algebras and Their Representations'' (jointly with Joseph A. Wolf and Geoffrey Mason). 
20092012  DFG grant (one postdoc position). 
2009  Volkswagen Foundation grant for organizing the summer school "Structures in Lie Representation Theory" (jointly with A. Joseph and A. Melnikov). 
20092015  DFG grant within the Schwerpunktprogramm 1388 "Darstellungstheorie" 
20122013  DFG grant for GermanIsraeli cooperation 
20122015  DFG grant within the priority program "SPP 1388 Darstellungstheorie" 
20152016  AIM SQuaRE grant 
20152018  DFG grant (3/4 postdoc position). 
20182020  DFG grant (one postdoc position). 
Other Professional Activities:
19912006: Founding coorganizer of the California Lie Theory Program, a cooperation program in Lie Theory between the campuses of the University of California.
2004 : Coorganizer of the Program ”Darstellungstheorie, Transformationsgruppen und Mathematische Physik Eof the consortium of six universities: Jacobs University Bremen, University of Bochum, University of Erlangen, University of Hamburg, University of Koeln, and University of Paderborn.
2005: Coorganizer of the conference in honor of Yu. I. Manin at the Max Planck Institute for Mathematics, February 2005.
2005: Coorganizer of the International Conference in Honor of R.O. Wells, Jr., Jacobs University Bremen (formerly IUB), December 12, 2005.
2010: Coorganizer of the International Conference in "Infinitedimensional Lie Algebras" in Newfoundland, Canada
2011: Coorganizer of the conference "Lie Groups" in honor of J.A. Wolf, Bochum, Germany
2012: Coorganizer of the GermanIsraeli workshop "Symplectic Geometry with applications to Representation Theory" at Jacobs University, Bremen, Germany
2012: Organizer of the meeting "7 1/2" in honor of Yu. I. Manin at IHES, Bures sur Yvette, France
2013: Organizer of a conference in honor of V. Tsanov, Sofia, Bulgaria.
2014: Coorganizer of the annual meeting in Soltau of the priority program ``SPP 1388 Darstellungstheorie''.
2014: Coorganizer of the meeting ``Hodge theory and unitary representations of reductive Lie groups'', Jacobs University Bremen.
2015: Coorganizer of the meeting ``Groups and Rings Theory and Applications'', July 1522, Sofia, Bulgaria.
2019: Coorganizer of the meeting `` Perspectives on representations of semisimple Lie algebras: A workshop in honor of Gregg Zuckerman on the occasion of his 70th birthday'', May 2224, Bochum, Germany.
Academic Publications:
1.The Penrose transform on general grassmannians, C.R. Acad. Sci. Bulg. 33 (1980), 14391442.
2.Nullgeodesics of complex Einstein spaces, Funk. Anal. i Priloz. 16, No.1 (1982), 7879 (Russian), (with Yu.I.Manin).
3.Linear differential operators and cohomology of analytic spaces, Uspekhi Mat. Nauk 37, No 4 (1982), 171172 (Russian).
4.Dmodules on supermanifolds, Invent. Math. 71 (1983), 501512.
5.The formalism of left and right connections on supermanifolds, (1982). In: Lect. on supermanifolds, geom. methods and conf. groups, editors Döbner et al, World Scientific, Singapore, 1989, 313 (with Yu. I. Manin).
6.An introduction to geometric representation theory for complex simple Lie superalgebras. In: Proc. Conf. Diff. Geom. Math. in Physics, Shumen 1984, World Scientific 1986, 89106.
7.Serre duality for projective supermanifolds, Funk. Anal. i Priloz. 18,No.1 (1984), 7879, (Russian) (with O. Ogievetsky).
8.Projectivity and Daffinity of flag supermanifolds, Uspekhi Math. Nauk 40 No.1 (1985), 211212, (Russian) (with I. Skornyakov).
9.A geometric approach to the linear Penrose transform, Transactions AMS 290 (1985), 555575.
10.Cohomologie des Dmodules typiques sur les supervariétés de drapeaux, C. R. Acad. Sci. Paris 199 (1984), 10051008 (with I. Skornyakov).
11.Characters of typical irreducible finite dimensional modules, Funk. Anal. i Priloz. 20 (1986), No. 1, 3745 (Russian).
12.Localisation des representations typiques d'une superalgèbre de Lie complexe classique, C. R. Acad. Sci. Paris 304 (1987), 163166.
13.BorelWeilBott theory for classical Lie supergroups. In: Curr. Probl. Math., Moscow, vol. 32 (1988), 71124 (Russian).
14.Elements of supergeometry. In: Curr. Probl. Math., Moscow, vol. 32 (1988), 325, (Russian), (with Yu. I. Manin and A. Voronov).
15.Character formulas for some classes of atypical and modules, Lett. Math. Phys. 16 (1988), 251261 (with V. Serganova).
16.Cohomology of for classical complex Lie supergroups and characters of some atypical Gmodules, Annales Fourier 39 (1989), 845873, (with V. Serganova).
17.Generic irreducible representations of classical Lie superalgebras. In: Lecture Notes in Physics, vol. 375 (1991), Springer Verlag, Berlin, 311319 (with V. Serganova).
18.Representations of classical Lie superalgebras of type 1, Indag. Math., N.S. 3(2), (1992), 419466 (with V. Serganova).
19.Generic representations of classical Lie superalgebras and their localisation, Monatsh. Math. 118 (1994), 267313.
20.Generic irreducible representations of finitedimensional Lie superalgebras, Intern. Journ. Math. 5 (1994), 389419 (with V. Serganova).
21.Partially and fully integrable modules over Lie superalgebras. In: Studies in Advanced Mathematics (series editor S.T. Yau), vol. 4, AMS and Internatl. Press 1997, 4967 (with I. Dimitrov).
22.Characters of irreducible modules and cohomology of for the Lie supergroup , Journ. of Math. Sci. 84 (1997), 13821412 (with V. Serganova).
23.Characters of finitedimensional irreducible modules, Lett. Math. Phys. 40 (1997), 147158 (with V. Serganova).
24.Characters of strongly generic irreducible Lie superalgebra representations, Intern. Journ. Math. 9 (1998), 331366.
25.Partially integrable highest weight modules, Transformation Groups 3 (1998), 241253 (with I. Dimitrov).
26.The support of an irreducible Lie algebra representation, Journ. of Algebra 209 (1998), 129142 (with V. Serganova).
27.Weight modules of direct limit Lie algebras, IMRN 1999, no. 5, 223249 (with I. Dimitrov).
28.Weight representations of the Cartan type Lie algebras and , Math. Research Lett. 6 (1999), 397416 (with V. Serganova).
29.On the structure of weight modules, Transactions AMS 352 (2000), 28572869 (with I. Dimitrov and O. Mathieu).
30. Generalized HarishChandra modules, Moscow Math. Journal 2 (2002), 753767 (with V. Serganova).
34. Finite rank vector bundles on inductive limits of grassmannians, IMRN 2003, no. 34, 18711887 (with J. Donin).
35. Classically semisimple locally finite Lie superalgebras, Forum Math. 16 (2004), 431446.
36.On the existence of (g,k)modules of finite type, Duke Math. Journal 125 (2004), 329349 (with V. Serganova and G. Zuckerman).
37.A Reduction Theorem for Highest Weight Modules over Toroidal Lie Algebras, Comm. Math. Physics 250(2004), no. 1, 4753 (with I. Dimitrov and V. Futorny).
38.Generalized HarishChandra modules: a new direction of the structure theory of representations, Acta Applicandae Mathematicae, 81(2004), 311326(with G. Zuckerman).
39. Indvarieties of generalized flags as homogeneous spaces for classical indgroups, IMRN 2004, no. 55, 29352953 (with I. Dimitrov).
40. Borel subalgebras of , Resenhas IMEUSP 6 (2004),111119 (with I. Dimitrov).
41. Generalized HarishChandra modules with generic minimal ktype, Asian Journal of Mathematics 8(2004), 795812 (with G. Zuckerman)
42. A construction of generalized HarishChandra modules with arbitrary minimal ktype, Canad. Math. Bull. 50 (2007), 603609 (with G. Zuckerman).
43. Cartan subalgebras of rootreductive Lie algebras, Journ. of Algebra, 308(2007), 583611 (with E. DanCohen and N. Snyder).
44. A construction of generalized HarishChandra modules for locally reductive Lie algebras, Transformation Groups 13 (2008), 799817 (with G. Zuckerman).
45. Locally semisimple and maximal subalgebras of the finitary Lie algebras \(\mathfrak{gl}(\infty), \mathfrak{sl}(\infty), \mathfrak{so}(\infty)\), and \(\mathfrak{sp}(\infty)\), Journal of Algebra 322 (2009), 20692081 (with I. Dimitrov)
46. Parabolic and Levi subalgebras of finitary Lie algebras, IMRN, International Mathematics Research Notices, Article ID rnp169, doi:10.1093/imrn/rnp169 (with E. DanCohen)
47. Parabolic Subgroups of Real Direct Limit Lie Groups. In: Contemporary Mathematics, vol. 499, AMS 2009 (with E. DanCohen and J. A. Wolf)
48. Rank 2 vector bundles on indgrassmannians.In, Manin Festschrift, Progress in Mathematics 270, Birkhaeuser Boston, 2009, 555572 (with A. S. Tikhomirov).
49. Bounded simple (g; sl(2))modules for rkg = 2, Journal of Lie Theory 20 (2010), 581615 (with V. Serganova).
50. Tensor representations of infinitedimensional rootreductive Lie algebras. In: Developments and Trends in InfiniteDimensional Lie Theory, Progress in Mathematics 288, Birkh\"auser, 2011, 127150 (with K. Styrkas).
51. On bounded generalized HarishChandra modules, Annales de l'Institut Fourier, 62(2012), 477496 (with V. Serganova).
52. Triviality of vector bundles on twisted indGrassmannians, Mat. Sbornik 202:1 (2011), 139 (with A. S. Tikhomirov).
53. A BottBorelWeil theorem for diagonal indgroups, Canadian Journal of Mathematics, doi:10.4153/CJM20110326 (with I. Dimitrov).
54. Categories of integrable $sl(\infty)$, $o(\infty)$, $sp(\infty)$modules. In: Representation Theory and Mathematical Physics, Contemporary Mathematics 557, AMS 2011, 335357 (with V. Serganova).
55. Levi components of parabolic subalgebras of finitary Lie algebras, arXiv:1008.0311v1, in Representation Theory and Mathematical Physics, Contemporary Mathematics, vol. 557, AMS 2011, 129149 (with E. DanCohen).
56. A Koszul category of representations of finitary Lie algebras, Advances of Mathematics 289 (2016), 250278 (with E. DanCohen and V. Serganova).
57. On the structure of the fundamental series of generalized HarishChandra modules, Asian Journal of Mathematics 16 (2012), 489514 (with G. Zuckerman).
58. On Ideals in the enveloping algebra of a locally simple Lie algebra, Int Math Res Notices 2015 (2015), 51965228 (with A. Petukhov).
59. Linear indGrassmannians, Pure and Applied Math. Quarterly 10 (2014), 289323 (with A. Tikhomirov).
60. Algebraic methods in the theory of generalized HarishChandra modules. In: Developments and Retrospectives in Lie Theory: Algebraic Methods, Developments in Mathematics, vol. 38, Springer Verlag, 2014, 331350 (with G. Zuckerman).
61. Tensor representations of Mackey Lie algebras and their dense subalgebras. In: Developments and Retrospectives in Lie Theory: Algebraic Methods, Developments in Mathematics, vol. 38, Springer Verlag, 291330 (with V. Serganova).
62. On the BarthVan de VenTyurinSato Theorem, Sbornik: Mathematics, 206:6 (2015), 814848 (with A. Tikhomirov).
63. A categorification of the bosonfermion correspondence via representation theory of $sl(\infty)$, Comm. Math. Phys., 341:3 (2016), 911931 (with I. Frenkel and V. Serganova).
64. Annihilators of highest weight $sl(\infty)$modules, Transformation Groups 21 (2016), 821849 (with A. Petukhov).
65. Infinite Konstant cascades and centrally generated primitive ideals of U(n) in types A_∞, C_∞, Journal of Algebra 447(2016), 109134 (with M. Ignatyev).
66. Schubert decompositions for indvarieties of generalized flags, Asian Journal of Mathematics 21 (2017), 599630 (with L. Fresse).
67. On ideals in U(sl(∞)), U(o(∞)), U(sp(∞)). In: Representation theory  current trends and perspectives, EMS Series of Congress Reports, European Mathematical Society (EMS), 2016, 565602 (with A. Petukhov).
68. Ordered tensor categories and representations of the Mackey Lie algebra of infinite matrices, Algebra and Representation Theory (2018), DOI:10.1007/s1046801897659, arXiv:1512.08157 (with A. Chirvasitu).
69. Real group orbits on flag indvarieties of SL(∞,ℂ). In: Lie Theory and Its Applications in Physics, Springer Proceedings in Mathematics and Statistics, vol. 191 (2016), 111135 (with M. V. Ignatyev and J. A. Wolf), corrected version.
70. On categories of admissible \(\big(\mathfrak{g},\mathrm{sl}(2)\big)\)modules, Transformation Groups 23(2) (2018), 463489(with V. Serganova and G. Zuckerman).
71. Primitive ideals of \(\mathrm{U}\big(\mathfrak{sl}(\infty)\big)\), Bulletin LMS 50 (2018), 443448 (with A. Petukhov).
72. Indvarieties of generalized flags: a survey of results, arXiv:1701.08478, preprint 2016 (with M. Ignatyev).
72'. Indvarieties of generalized flags: a survey of results. In:'' Itogi nauki i techniki, series Modern mathematics and its applications'', Russian Academy of Sciences 2018, Topic Surveys 147, 350, (with M. Ignatyev), Russian version.
73. Decomposition of cohomology of vector bundles on homogeneous indspaces, C. R. Acad. Sci. Bulg. 70:7 (2017), 907916 (with E. Hristova).
74. Orbit duality in indvarieties of maximal generalized flags, Transactions of the Moscow Mathematical Society, 2017, 131160 (with L. Fresse).
74'. Orbit duality in indvarieties of maximal generalized flags, Transactions of the Moscow Mathematical Society 78 (2017), no 1(with L. Fresse), Russian version, arXiv:1704.03671.
75. Representation categories of Mackey Lie algebras as universal monoidal categories, Pure and Applied Mathematics Quarterly 13 (2017), 77121 (with A. Chirvasitu).
76. Primitive ideals of \(\mathrm{U}\big(\mathfrak{sl}(\infty)\big)\) and the RobinsonSchensted algorithm at infinity, arXiv:1801.06692, to appear in Representation of Lie Algebraic Systems and Nilpotent orbits, Progress in Mathematics, Birkhauser (with A. Petukhov).
77. Integrable \(\mathfrak{sl}(\infty)\)modules and category \(\mathcal{O}\) for \(\mathfrak{gl}(mn)\), Journal LMS, DOI: 10.1112/jlms.12176, arXiv:1712.00664 (with C. Hoyt and V. Serganova).
78. On an infinite limit of BGG categories \(\mathcal{O}\), Moscow Mathematical Journal, to appear; arXiv:1802.06343 (with K. Coulembier).
79. On the existence of infinitedimensional generalized HarishChandra modules, SaoPaulo Jour. Math. 12(2018), 290294(with G. Zuckerman).
80. Simple bounded weight modules of \(\mathfrak{sl}_{\infty}\), \(\mathfrak{o}_{\infty}\), \(\mathfrak{sp}_{\infty}\), arXiv:1807.01899, preprint 2018 (with D. Grantcharov).
81. Large annihilator category \(\mathcal{O}\) for \(\mathfrak{sl}_{\infty}\), \(\mathfrak{o}_{\infty}\), \(\mathfrak{sp}_{\infty}\), Journal of Algebra, to appear; arXiv:1809.09394 (with V. Serganova).
82. Examples of automorhism groups of indvarieties of generalized flags, Journal of Geometry and Symmetry in Physics 50(2018), 7177(doi:10.7546/jgsp5020187177)
Books edited:
1. V. Chari, I. B. Penkov  editors. Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras. Studies in Advanced Mathematics, vol. 4, 1997, AMS.
2. A. Joseph, A. Melnikov, I. Penkov  editors. Highlights in Lie Algebraic Methods. Progress in Mathematics, vol. 295, 2011, Birkhauser.
3. A. Huckleberry, I. Penkov, G. Zuckerman  editors. Lie Groups: Structure, Actions, and Representations. Progress in Mathematics, vol. 306, 2013, Birkhauser.
4. G. Mason, I. Penkov, J.A. Wolf  editors. Developments and Retrospectives in Lie Theory: Geometric and Analytic Methods, Developments in Mathematics, vol.37, 2014, Springer Verlag.
5. G. Mason, I. Penkov, J.A. Wolf  editors. Develpoments and Retrospectives in Lie Theory: Algebraic Methods, Developments in Mathematics, vol. 38, 2014, Springer Verlag.
Special journal issues edited:Sao Paulo Journal of Mathematical Sciences, vol. 12(2018), issue 2 (jointly with A.Huckleberry).