Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

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DMV Tagung 2011 - Köln, 19. - 22. September Montag, 19. September Philosophikum, S91 14:00 Paolo Papi (Università di Roma “La Sapienza”) Denominator identities for finite-dimensional Lie superalgebras 15:00 Pierluigi Möseneder Frajria (Politecnico die Milano) Superalgebras and Theta correspondence over the real numbers 16:00h – 16:30h Pause 16:30 Hadi Salmasian (University of Ottawa) An analytic approach to unitary representations of Lie supergroups 17:30 Fabio Gavarini (Università degli Studi die Roma “Tor Vergata”) Algebraic supergroups associated to simple Lie superalgebras Dienstag, 20. September Philosophikum, S91 14:00 Volodymyr Mazorchuk (Uppsala University) Serre functors for Lie superalgebras 15:00 Joris Van der Jeugt (Gent University) Wigner quantization and representations of Lie superalgebras 16:00h – 16:30h Pause 16:30 Shun-Jen Cheng (Academia Sinica, Taiwan) Kostant homology formula for oscillator representations of classical Lie superalgebras 17:30 Weiqiang Wang (University of Virginia) A super duality approach to the representation theory of Lie superalgebras Mittwoch, 21. September Philosophikum, S91 14:00 Vera Serganova (University of California at Berkeley) Borel-Weil-Bott theorem and Bernstein-Gelfand-Gelfand reciprocity for classical supergroups 15:00 Catharina Stroppel (Universität Bonn) t.b.a. 132
DMV Tagung 2011 - Köln, 19. - 22. September Shun-Jen Cheng Academia Sinica, Taiwan Kostant homology formula for oscillator representations of classical Lie superalgebras Pierluigi Möseneder Frajria Politecnico di Milano Superalgebras and Theta correspondence over the real numbers The odd part of the super denominator of a basic classical Lie superalgebra is the character of the oscillator representation of the odd part of the superalgebra. It is then natural to use superalgebra techniques to study this representation. In particular, we will show how the generalized denominator formulas for basic classical Lie superalgebras can be used to derive the Theta correspondence between representations of a compact dual pair. Fabio Gavarini Università degli Studi di Roma “Tor Vergata” Algebraic supergroups associated to simple Lie superalgebras For any finite dimensional (complex) simple Lie superalgebra I provide an explicit recipe to construct an algebraic supergroupe G (defined via its functor of points) whose tangent Lie superalgebra is g itself.To do that, I generalise the classical Chevalley method, which constructs a (semi-) simple algebraic group starting from any complex, f. d. (semi-) simple Lie algebra g and from a faithful f. d. g-module V: the basic ingredient to make use of is the datum of a so-called “Chevalley basis”. I shall show that one can do the same when g is replaced with a simple Lie superalgebra: one introduces then a notion of “Chevalley basis”, one proves the existence of the latter, and then one essentially implements the same method (with many new aspects to deal with, of course). A remarkable fact is that this strategy is succesful both with the (simple) Lie superalgebras of classical type and with those of Cartan type—somehow extending the range of application of Chevalley’s original idea. Besides this “existence” result, I shall present also a “uniqueness” one: every connected algebraic supergroup whose Lie superalgebra be (f.d.) simple is isomorphic to one of the supergroups that I just constructed. Thus one eventually finds a complete classification of such supergroups. Literatur Fioresi, R., Gavarini, F. (2011). Chevalley Supergroups. Mem. Amer. Math. Soc., in press. ar- Xiv:0808.0785. Gavarini, F. (2008). Chevalley Supergroups of type D(2,1;a). arXiv:1008.1838. Fioresi, R., Gavarini, F. (2010). On the construction of Chevalley Supergroups. In: Supersymmetry in Mathematics and Physics, Lect. Notes Math., to appear. arXiv:1008.1838. Fioresi, R., Gavarini, F. Algebraic supergroups with classical Lie superalgebras, in preparation. Gavarini, F. Algebraic supergroups of Cartan type, in preparation. 133
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Felix Schulze Freie Universität Be
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Eleutherius Symeonidis Katholische
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Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

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