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

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.