Representation Theory: Boundary q-characters of finite-dimensional representations of quantum affine symmetric pairs

Speaker:Jian-Rong Li (University of Vienna)

Time: 2025-10-23 14:00-16:00
Location: 1010, SIMIS

摘要：
Frenkel and Reshetikhin introduced q-characters for finite-dimensional representations of quantum affine algebras, providing a fundamental tool in their representation theory. Boundary q-characters for finite dimensional representations of quantum affine symmetric pairs of split types were introduced and developed by Tomasz Przezdziecki and myself. In this talk, I will present a new joint work Tomasz Przezdziecki on evaluation modules for split quantum affine symmetric pairs. By computing the action of generators in Lu and Wang’s Drinfeld-type presentation on Gelfand–Tsetlin bases, we determine the spectrum of a large commutative subalgebra arising from this presentation. This leads to an explicit formula for boundary analogues of q-characters, which we interpret combinatorially in terms of semistandard Young tableaux. Our results show that boundary q-characters share familiar features with ordinary q-characters—such as a version of the highest weight property—while also exhibiting new phenomena, including an additional symmetry.