April 29 : Martina Lanini

Title: The Steinberg-Lusztig tensor product theorem for abstract Fock space

Abstract:

The abstract Fock space, constructed in joint work with A.Ram and P.Sobaje, is a combinatorial gadget which generalizes Lecler-Thibon's realization of the classical Fock Space to any Lie type, and encodes decomposition numbers for quantum groups at roots of unity. In this talk I will discuss joint work with Arun Ram, in which we establish the analogue of the Steinberg-Lusztig Tensor product Theorem for abstract Fock space. This result has several consequences, such as a new proof of the Casselman-Shalika formula, and a character formula for a certain class of modules for affine Kac-Moody algebras at a negative level.