Anton Zeitlin, LSU – Physically Inspired Mathematics Seminar

Title: q-opers, QQ-systems, and q-Langlands correspondence.

Abstract: The well-known relation between a certain class of connections (opers) with regular singularities on projective line without monodromy and the  Bethe equations for Gaudin models serves as an example of geometric Langlands correspondence.  In this talk I will describe q-deformation of this example. The central object in the construction is the multiplicative version of opers, group-valued objects, which we refer to аs q-opers. Here will be described their relation to the so-called QQ-systems, studied in representation-theoretic context by E. Frenkel and D. Hernandez and the Bethe equations for XXZ model.  We also put  q-opers  in the context of quantum q-Langlands correspondence recently outlined by M. Aganagic, E. Frenkel, and A. Okounkov, and related structures of enumerative geometry.

Based on a joint work with E. Frenkel, P. Koroteev and D. Sage.