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Characters of representations of Lie (super)algebras and (mock)theta functions

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V. Kac
Mon, 2015-03-23 09:00 - 10:15
MPIM Lecture Hall

Understanding of the Weyl character formula, universal enveloping algebra and Verma modules.
Knowledge of some elements of Lie superalgebra theory.
Knowledge of some elements of Jacobi theta functions and modular forms.
1. Lie superalgebras
2. Ane Lie (super)algebras: loop and KM constructions
3. Character formula for integrable and admissible representations in the Lie algebra case and Jacobi
theta functions
4. Character formula for tame integrable and admissible modules in the Lie superalgebra case and
mock theta functions
5. Modular invariance of normalized characters for integrable representations of ane Lie algebras
6. Modular invariance of modi ed normalized characters of tame integrable modules over ane Lie
7. Branching functions are modular functions for ane Lie algebras
8. Branching functions are "half" modular functions for ane Lie superalgebras
9. Quantum Hamiltonian reduction for ane Lie (super)algebras and modular invariance of modi ed
characters for (super)conformal algebras
(7-9 time permitting)
V.G.Kac, Lie superalgebras, Adv. Math. 26(1977),8-96. V.G.Kac, In nite-dimensional Lie alge-
bras, third ed, Cambridge University Press, 1990.
V.G.Kac, D.H.Peterson, Ane Lie algebras and Hecke inde nite modular forms, Bull.Amer.Math.Soc.
V.G.Kac, D.H.Peterson, In nite-dimensional Lie algebras, theta functions and modular forms, Adv.
Math. 53(1984),125-264.
V.G.Kac, M.Wakimoto, Modular invariant representations of in nite-dimensional Lie algebras and
superalgebras, Proc. Nat.Acad.Sci.USA 85(1988),4956-4960.
V.G.Kac, M.Wakimoto, Integrable highest weight representations over ane superalgebras and
Appell's function, Comm.Math.Phys. 215(2001),631-682.
V.G.Kac, M.Wakimoto, Representations of ane superalgebras and mock theta functions, Transf.
Groups 19(2014),383-455.

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