Asymptotics of standard modules of quantum affine algebras

Abstract

Finite dimensional representations of quantum affine algebras have a behavior similar to the Kazhdan-Lusztig conjecture. Nakajima showed that characters of standard modules can be expressed as linear combinations of characters of simple modules of lower weight. Moreover, the coefficients are non-negative and can be expressed as evaluation of some polynomials. In our work, we want to obtain the same type of results for the category O of representations of a Borel subalgebra (introduced by Hernandez-Leclerc). In this talk, we will present the motivation behind the definition of our asymptotical standard modules, as well as an idea for their construction in the case where g is affine sl2.

Date
May 24, 2018
Location
University of California, Riverside
Riverside, USA
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Léa Bittmann
Research Associate