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Curriculum Vitae
IVAN B. PENKOV
Personal: US citizen, born May 19, 1957 in Sofia, Bulgaria, married with two children. University Education:
Research and Teaching Positions:
Main Research Interests:
Other Professional Activities: 1991--2006: 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 1-2, 2005. 2010: Coorganizer of the International Conference in "Infinite-dimensional Lie Algebras" in Newfoundland, Canada 2011: Coorganizer of the conference "Lie Groups" in honor of J.A. Wolf, Bochum, Germany 2012: Coorganizer of the German-Israeli 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 15-22, 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 22-24, Bochum, Germany.
Academic Publications:
1.The Penrose transform on general grassmannians,
C.R. Acad. Sci. Bulg. 33 (1980), 1439-1442.
2.Null-geodesics of complex Einstein
spaces,
Funk. Anal. i Priloz. 16, No.1 (1982), 78-79 (Russian), (with
Yu.I.Manin).
3.Linear differential operators and cohomology of
analytic spaces, Uspekhi Mat. Nauk 37, No 4 (1982), 171-172
(Russian).
4.D-modules on supermanifolds, Invent. Math. 71
(1983), 501-512.
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, 3-13 (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,
89-106.
7.Serre duality for projective supermanifolds,
Funk. Anal. i Priloz. 18,No.1 (1984), 78-79, (Russian) (with O.
Ogievetsky).
8.Projectivity and D-affinity of flag
supermanifolds, Uspekhi Math. Nauk 40 No.1 (1985), 211-212,
(Russian) (with I. Skornyakov).
9.A geometric approach to the linear Penrose
transform, Transactions AMS 290 (1985), 555-575.
10.Cohomologie des D-modules typiques sur les
supervariétés de drapeaux, C. R. Acad. Sci. Paris 199
(1984), 1005-1008 (with I. Skornyakov).
11.Characters of typical irreducible finite
dimensional
12.Localisation des representations typiques d'une
superalgèbre de Lie complexe classique, C. R. Acad. Sci. Paris
304 (1987), 163-166.
13.Borel-Weil-Bott theory for classical Lie
supergroups. In: Curr. Probl. Math., Moscow, vol. 32 (1988), 71-124
(Russian).
14.Elements of supergeometry. In: Curr. Probl. Math.,
Moscow, vol. 32 (1988), 3-25, (Russian), (with Yu. I. Manin and A.
Voronov).
15.Character formulas for some classes of atypical
16.Cohomology of
17.Generic irreducible representations of
classical Lie superalgebras. In: Lecture Notes in Physics, vol. 375 (1991),
Springer Verlag, Berlin, 311-319 (with V. Serganova).
18.Representations of classical Lie superalgebras
of type 1, Indag. Math., N.S. 3(2), (1992), 419-466 (with V.
Serganova).
19.Generic representations of classical Lie
superalgebras and their localisation, Monatsh. Math. 118 (1994),
267-313.
20.Generic irreducible representations of
finite-dimensional Lie superalgebras, Intern. Journ. Math. 5
(1994), 389-419 (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, 49-67 (with I.
Dimitrov).
22.Characters of irreducible
23.Characters of finite-dimensional irreducible
24.Characters of strongly generic irreducible Lie
superalgebra representations, Intern. Journ. Math. 9 (1998),
331-366.
25.Partially integrable highest weight modules,
Transformation Groups 3 (1998), 241-253 (with I. Dimitrov).
26.The support of an irreducible Lie algebra
representation, Journ. of Algebra 209 (1998), 129-142 (with V.
Serganova).
27.Weight modules of direct limit Lie algebras,
IMRN 1999, no. 5, 223-249 (with I. Dimitrov).
28.Weight representations of the Cartan type Lie
algebras
29.On the structure of weight modules,
Transactions AMS 352 (2000), 2857-2869 (with I. Dimitrov and O.
Mathieu).
30. Generalized Harish-Chandra modules, Moscow Math.
Journal 2 (2002), 753-767 (with V. Serganova).
34. Finite rank vector bundles on inductive limits of grassmannians, IMRN 2003, no. 34, 1871-1887 (with J. Donin).
35. Classically semisimple locally finite Lie superalgebras, Forum Math. 16 (2004), 431-446.
36.On the existence of (g,k)-modules of finite
type, Duke Math. Journal 125 (2004), 329-349
(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, 47-53 (with I. Dimitrov and V. Futorny).
38.Generalized Harish-Chandra modules: a new direction of
the structure theory of representations, Acta Applicandae Mathematicae,
81(2004), 311-326(with G. Zuckerman).
39. Ind-varieties of generalized flags as homogeneous spaces for classical ind-groups, IMRN 2004, no. 55, 2935-2953 (with I. Dimitrov).
40. Borel subalgebras of
41. Generalized Harish-Chandra modules with generic minimal k-type, Asian Journal of Mathematics 8(2004), 795-812 (with G. Zuckerman)
42. A construction of generalized Harish-Chandra modules with arbitrary minimal k-type, Canad. Math. Bull. 50 (2007), 603-609 (with G. Zuckerman).
43. Cartan subalgebras of root-reductive Lie algebras, Journ. of Algebra, 308(2007), 583-611 (with E. Dan-Cohen and N. Snyder).
44. A construction of generalized Harish-Chandra modules for locally reductive Lie algebras, Transformation Groups 13 (2008), 799-817 (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), 2069-2081 (with I. Dimitrov)
46. Parabolic and Levi subalgebras of finitary Lie algebras, IMRN, Article ID rnp169,
doi:10.1093/imrn/rnp169 (with E. Dan-Cohen)
47. Parabolic Subgroups of Real Direct Limit Lie Groups. In: Contemporary Mathematics, vol. 499, AMS 2009 (with E. Dan-Cohen and J. A. Wolf)
48. Rank 2 vector bundles on ind-grassmannians.In, Manin Festschrift, Progress in Mathematics 270, Birkhaeuser Boston, 2009, 555-572 (with A. S. Tikhomirov).
49. Bounded simple (g; sl(2))-modules for rkg = 2, Journal of Lie Theory 20 (2010), 581-615 (with V. Serganova).
50. Tensor representations of classical locally finite Lie algebras. In: Developments and Trends in Infinite-Dimensional Lie Theory, Progress in Mathematics 288, Birkh\"auser, 2011, 127-150 (with K. Styrkas).
51. On bounded generalized Harish-Chandra modules, Annales de l'Institut Fourier, 62(2012), 477-496 (with V. Serganova).
52. Triviality of vector bundles on twisted ind-Grassmannians, Mat. Sbornik 202:1 (2011), 1-39 (with A. S. Tikhomirov).
53. A Bott-Borel-Weil theorem for diagonal ind-groups, Canadian Journal of Mathematics, doi:10.4153/CJM-2011-032-6 (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, 335-357 (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, 129-149 (with E. Dan-Cohen).
56. A Koszul category of representations of finitary Lie algebras, Advances of Mathematics 289 (2016), 250-278 (with E. Dan-Cohen and V. Serganova).
57. On the structure of the fundamental series of generalized Harish-Chandra modules, Asian Journal of Mathematics 16 (2012), 489-514 (with G. Zuckerman).
58. On Ideals in the enveloping algebra of a locally simple Lie algebra, IMRN 2015 (2015), 5196-5228 (with A. Petukhov).
59. Linear ind-Grassmannians, Pure and Applied Math. Quarterly 10 (2014), 289-323 (with A. Tikhomirov).
60. Algebraic methods in the theory of generalized Harish-Chandra modules. In: Developments and Retrospectives in Lie Theory: Algebraic Methods, Developments in Mathematics, vol. 38, Springer Verlag, 2014, 331-350 (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, 291-330 (with V. Serganova), corrected version.
62. On the Barth-Van de Ven-Tyurin-Sato Theorem, Sbornik: Mathematics, 206:6 (2015), 814-848 (with A. Tikhomirov).
63. A categorification of the boson-fermion correspondence via representation theory of $sl(\infty)$, Comm. Math. Phys., 341:3 (2016), 911-931 (with I. Frenkel and V. Serganova).
64. Annihilators of highest weight $sl(\infty)$-modules, Transformation Groups 21 (2016), 821-849 (with A. Petukhov).
65. Infinite Kostant cascades and centrally generated primitive ideals of U(n) in types A_∞, C_∞, Journal of Algebra 447(2016), 109-134 (with M. Ignatyev).
66. Schubert decompositions for ind-varieties of generalized flags, Asian Journal of Mathematics 21 (2017), 599-630 (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, 565-602 (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/s10468-018-9765-9, arXiv:1512.08157 (with A. Chirvasitu).
69. Real group orbits on flag ind-varieties of SL(∞,ℂ). In: Lie Theory and Its Applications in Physics, Springer Proceedings in Mathematics and Statistics, vol. 191 (2016), 111-135 (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), 463-489(with V. Serganova and G. Zuckerman).
71. Primitive ideals of \(\mathrm{U}\big(\mathfrak{sl}(\infty)\big)\), Bulletin LMS 50 (2018), 443-448 (with A. Petukhov).
72. Ind-varieties of generalized flags: a survey of results, Journal of Mathematical Sciences 248 (2020), 255–302 (with M. Ignatyev).
72'. Ind-varieties 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, 3-50, (with M. Ignatyev), Russian version.
73. Decomposition of cohomology of vector bundles on
homogeneous ind-spaces, C. R. Acad. Sci. Bulg. 70:7 (2017), 907-916 (with E. Hristova).
74. Orbit duality in ind-varieties of maximal generalized flags, Transactions of the Moscow Mathematical Society, 2017, 131-160 (with L. Fresse).
74'. Orbit duality in ind-varieties 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), 77-121 (with A. Chirvasitu).
76. Primitive ideals of \(\mathrm{U}\big(\mathfrak{sl}(\infty)\big)\)
and
the Robinson-Schensted algorithm at infinity, In: Representation of Lie Algebraic Systems and Nilpotent orbits, Progress in Mathematics 330 (2019), Birkhäuser, 471-499 (with A. Petukhov).
77.
Integrable \(\mathfrak{sl}(\infty)\)-modules and category \(\mathcal{O}\) for \(\mathfrak{gl}(m|n)\), Journal LMS 99 (2019), 403-427 (with C. Hoyt and V. Serganova).
78. On an infinite limit of BGG categories \(\mathcal{O}\), Moscow Mathematical Journal 19 (2019), 655-693 (with K. Coulembier).
79. On the existence of infinite-dimensional generalized Harish-Chandra modules, Sao-Paulo Journ. Math. 12 (2018), 290-294 (with G. Zuckerman).
80. Simple bounded weight modules of \(\mathfrak{sl}_{\infty}\), \(\mathfrak{o}_{\infty}\), \(\mathfrak{sp}_{\infty}\), Transformation Groups 25(4) (2020), 1125-1160 (with D. Grantcharov).
81. Large annihilator category \(\mathcal{O}\) for \(\mathfrak{sl}_{\infty}\), \(\mathfrak{o}_{\infty}\), \(\mathfrak{sp}_{\infty}\), Journal of Algebra 532 (2019), 249-279 (with V. Serganova).
82. Examples of automorphism groups of ind-varieties of generalized flags, Journal of Geometry and Symmetry in Physics 50 (2018), 71-77.
83. An algebraic-geometric construction of ind-varieties of generalized flags, Annali di Matematica Pura ed Applicata 201 (2022), 2287–2314 (with A. Tikhomirov).
84. Multiple flag ind-varieties with finitely many orbits, Transformation groups 27 (2022), 833–865 (with L. Fresse).
85. Integrable bounded weight modules of classical Lie superalgebras at infinity, Journal of Pure and Applied Algebra 226 (2022), 106847 (with L. Calixto).
86. Universal tensor categories generated by dual pairs, Applied Categorical Structures 29 (5), 915-950 (with A. Chirvasitu).
87. Automorphism groups of ind-varieties of generalized flags, Transformation groups (2022), doi:10.1007/s00031-022-09703-1 (with M. Ignatyev).
88. Bounded weight modules for basic classical Lie superalgebras at infinity, arXiv:2205.07138 (with D. Grantcharov and V. Serganova).
89. Topological tensor representations of \(\mathfrak{gl}(V)\) for a space \(V\) of countable dimension, Algebraic Geometry and Physics, to appear, arXiv:2206.00654 (with F. Esposito).
90. Topological semiinfinite tensor (super)modules, arXiv:2301.08921 (with F. Esposito).
91. On homogeneous spaces for diagonal ind-groups, arXiv:2303.18146 (with L. Fresse).
1. Classical Lie algebras at infinity, Springer Monographs in Mathematics, 2022, ISBN 978-3-030-89659-1 (with C. Hoyt).
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.
Sao Paulo Journal of Mathematical Sciences, vol. 12(2018), issue 2 (jointly with A.Huckleberry).
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-modules, Funk. Anal. i Priloz. 20 (1986),
No. 1, 37-45 (Russian).
-and 
-modules, Lett. Math. Phys. 16
(1988), 251-261 (with V. Serganova).
for classical complex Lie
supergroups 
and characters of some atypical G-modules, Annales
Fourier 39 (1989), 845-873, (with V. Serganova).
, Journ. of
Math. Sci. 84 (1997), 1382-1412 (with V. Serganova).
-modules, Lett. Math. Phys. 40 (1997), 147-158 (with V.
Serganova).
and 
, Math. Research Lett. 6 (1999),
397-416 (with V. Serganova).
, Resenhas IME-USP 6 (2004),111-119 (with I. Dimitrov).