Geometric Representation Theory Seminar

Organizers：

Lin Chen, Will Donovan, Penghui Li, Peng Shan, Changjian Su, Wenbin Yan

Speaker：

Élie Casbi (University of Vienna)

Time：

Fri., 10:30-11:30 am, Dec. 12, 2025

Venue：

B627, Shuangqing Complex Building A

Title:

A geometric approach to rational identities arising from the representation theory of affine quantum groups

Abstract:

Let G be a semisimple complex Lie group of simply-laced type, B a Borel in G and T a maximal torus in B. In our last joint work with Jian-Rong Li, we exhibited new families of non-trivial rational identities arising from the representation theory of Uq(g_aff), the quantum affine algebra associated to the Lie algebra of G. This was achieved by constructing a ring homomorphism from the torus containing Frenkel-Reshetikin’s q-characters of finite-dimensional representations of Uq(g_aff) to the ring of regular functions on the regular locus of the Lie algebra of T. We will present a geometric proof of these identities using schemes recently introduced by Francone-Leclerc called spaces of (G,c)-bands. This provides a unified picture for our former results with Jian-Rong Li relating the rational identities obtained from q-characters to the map \bar{D} introduced by Baumann-Kamnitzer-Knutson in their study of the equivariant homology of Mirković-Vilonen cycles. This is joint work with Ryo Fujita and Jian-Rong Li.