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Papers of I. Penkov available in electronic format:

  • 30. Generalized Harish-Chandra modules, Moscow Math. Journal 2 (2002), 753-767 (with V. Serganova). download
  • 34. Finite rank vector bundles on inductive limits of grassmannians, IMRN 2003, no. 34, 1871-1887 (with J. Donin). download
  • 35. Classically semisimple locally finite Lie superalgebras, Forum Math. 16 (2004), 431-446. download
  • 36. On the existence of (g,k)-modules of finite type, Duke Math. Journal 125 (2004), 329-349 (with V. Serganova and G. Zuckerman). download
  • 39. Ind-varieties of generalized flags as homogeneous spaces for classical ind-groups, IMRN 2004, no. 55, 2935-2953 (with I. Dimitrov). download
  • 40. Borel subalgebras of $gl(\infty)$, Resenhas IME-USP 6 (2004),111-119 (with I. Dimitrov). download
  • 41. Generalized Harish-Chandra modules with generic minimal k-type, Asian Journal of Mathematics 8(2004), 795-812 (with G. Zuckerman) download
  • 42. A construction of generalized Harish-Chandra modules with arbitrary minimal k-type, Canad. Math. Bull. 50 (2007), 603-609 (with G. Zuckerman). download
  • 43. Cartan subalgebras of root-reductive Lie algebras, Journ. of Algebra, 308(2007), 583-611 (with E. Dan-Cohen and N. Snyder). download
  • 44. A construction of generalized Harish-Chandra modules for locally reductive Lie algebras, Transformation Groups 13 (2008), 799-817 (with G. Zuckerman). download
  • 45. Locally semisimple and maximal subalgebras of the finitary Lie algebras gl(\infty), sl(\infty), so(\infty), and sp(\infty), Journal of Algebra 322 (2009), 2069E081 (with I. Dimitrov) download
  • 46. Parabolic and Levi subalgebras of finitary Lie algebras, IMRN, International Mathematics Research Notices, Article ID rnp169, doi:10.1093/imrn/rnp169 (with E. Dan-Cohen) download
  • 47. Parabolic Subgroups of Real Direct Limit Lie Groups, Contemporary Mathematics 499, AMS 2009 (with E. Dan-Cohen and J. A. Wolf) download
  • 48. Rank 2 vector bundles on ind-grassmannians, Manin Festschrift,in Progress in Mathematics 270, Birkhaeuser Boston, 2009, pp. 555-572 (with A. S. Tikhomirov). download
  • 49. Bounded simple (g; sl(2))-modules for rkg = 2, Journal of Lie Theory 20 (2010), 581-615 (with V. Serganova). download
  • 50. Tensor representations of infinite-dimensional root-reductive Lie algebras, in Developments and Trends in Infinite-Dimensional Lie Theory, Progress in Mathematics 288, Birkh\"auser, 2011, pp. 127-150 (with K. Styrkas). download
  • 51. On bounded generalized Harish-Chandra modules, Annales de l'Institut Fourier, 62(2012), 477-496 (with V. Serganova). download
  • 52. Triviality of vector bundles on twisted ind-Grassmannians, Mat. Sbornik 202:1 (2011), 1-39 (with A. S. Tikhomirov). download
  • 53. A Bott-Borel-Weil theorem for diagonal ind-groups, Canadian Journal of Mathematics, doi:10.4153/CJM-2011-032-6 (with I. Dimitrov). download
  • 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). download
  • 55. Levi components of parabolic subalgebras of finitary Lie algebras, arXiv:1008.0311v1, in Representation Theory and Mathematical Physics, Contemporary Mathematics 557, AMS 2011, 129-149 (with Elizabeth Dan-Cohen). download
  • 56. A Koszul category of representations of finitary Lie algebras, Advances of Mathematics 289 (2016), 250-278 (with Elizabeth Dan-Cohen and Vera Serganova). download
  • 57. On the structure of the fundamental series of generalized Harish-Chandra modules, Asian Journal of Mathematics 16 (2012), 489-514 (with Gregg Zuckerman). download
  • 58. On Ideals in the enveloping algebra of a locally simple Lie algebra, Int Math Res Notices 2015 (2015), 5196-5228 (with A. Petukhov). download
  • 59. Linear ind-Grassmannians, Pure and Applied Math. Quarterly 10 (2014), 289-323 (with A. Tikhomirov). download
  • 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). download
  • 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). download
  • 62. On the Barth-Van de Ven-Tyurin-Sato Theorem, Sbornik: Mathematics, 206:6 (2015), 814-848 (with A. Tikhomirov). download
  • 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). download
  • 64. Annihilators of highest weight $sl(\infty)$-modules, Transformation Groups 21 (2016), 821-849 (with A. Petukhov). download
  • 65. Infinite Konstant cascades and centrally generated primitive ideals of U(n) in types A_∞, C_∞, Journal of Algebra 447(2016), 109-134 (with M. Ignatyev). download
  • 66. Schubert decompositions for ind-varieties of generalized flags, Asian Journal of Mathematics 21 (2017), 599-630 (with L. Fresse). download
  • 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). download
  • 68. Ordered tensor categories and representations of the Mackey Lie algebra of infinite matrices, Algebras and Representation Theory 22 (2019), 249-279 (with A. Chirvasitu). download
  • 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. download
  • 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). download
  • 71. Primitive ideals of \(\mathrm{U}\big(\mathfrak{sl}(\infty)\big)\), Bulletin LMS 50 (2018), 443-448 (with A. Petukhov). download
  • 72. Ind-varieties of generalized flags: a survey of results, arXiv:1701.08478, preprint 2016 (with M. Ignatyev). download
  • 72'. Ind-varieties of generalized flags: a survey of results, Russian Academy of Sciences 2018, Topic Surveys 147, 3-50, (with M. Ignatyev), Russian version. download
  • 73. Decomposition of cohomology of vector bundles on homogeneous ind-spaces, C. R. Acad. Bulg. 70:7 (2017), 907-916 (with E. Hristova). download
  • 74. Orbit duality in ind-varieties of maximal generalized flags, Transactions of the Moscow Mathematical Society, 2017, 131-160 (with L. Fresse). download
  • 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. download
  • 75. Representation categories of Mackey Lie algebras as universal monoidal categories, Pure and Applied Mathematics Quarterly 13 (2017), 77-121 (with A. Chirvasitu). download
  • 76. Primitive ideals of \(\mathrm{U}\big(\mathfrak{sl}(\infty)\big)\) and the Robinson-Schensted algorithm at infinity, arXiv:1801.06692, to appear in Representation of Lie Algebraic Systems and Nilpotent orbits, Progress in Mathematics, Birkhauser (with A. Petukhov). download
  • 77. Integrable \(\mathfrak{sl}(\infty)\)-modules and category \(\mathcal{O}\) for \(\mathfrak{gl}(m|n)\), Journal LMS, DOI: 10.1112/jlms.12176, arXiv:1712.00664 (with C. Hoyt and V. Serganova). download
  • 78. On an infinite limit of BGG categories \(\mathcal{O}\), Moscow Mathematical Journal, to appear; arXiv:1802.06343 (with K. Coulembier). download
  • 79. On existence of infinite-dimensional generalized Harish-Chandra modules, Sao-Paulo Jour. Math. 12(2018), 290-294(with G. Zuckerman). download
  • 80. Simple bounded weight modules of \(\mathfrak{sl}_{\infty}\), \(\mathfrak{o}_{\infty}\), \(\mathfrak{sp}_{\infty}\), arXiv:1807.01899, preprint 2018 (with D. Grantcharov). download
  • 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). download
  • 82. Examples of automorphism groups of ind-varieties of generalized flags, Journal of Geometry and Symmetry in Physics 50(2018),71-77 (doi:10.7546/jgsp-50-2018-71-77). download

Dissertations of former PhD students:

  • E. Hristova - Branching laws for tensor modules over classical locally finite Lie algebras. download
  • S. Markouski - On homomorphisms of diagonal Lie algebras. download
  • T. Milev - On root Fernando-Kac subalgebras of finite type. download
  • T. Nampaisarn - Categories \(\mathcal{O}\) for Dynkin Borel subalgebras of root-reductive Lie algebras. download
  • A. Petukhov - A geometric approach to the study of (g, k)-modules of finite type. download

Bachelor's theses:

  • A. Shemyakov - On the socle filtration of indecomposable injective objects of the category \(\mathbb{T}^3_{\mathfrak{gl}^M}\). download
  • P. Weiss - Non-rigidity of the tensor representations of gl_\infty. download
  • M. Zhang - Lie algebras of linear systems and their automorphisms. download
  • N. Zokirova - Non-rigidity of injective indecomposable tensor modules of $\mathfrak{sp}(\infty)$ and $\mathfrak{so}(\infty)$. download

© Prof. Ivan Penkov, 2019
Site last edited on: Jul 2019
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