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q-Opers, QQ-Systems and Bethe Ansatz

Algebraic Geometry

Speaker: Peter Koroteev, UC Berkeley
Location: 3106 MSB
Start time: Thu, Nov 14 2019, 1:10PM

I will show the equivalence between nondegenerate Z-twisted (G,q)-opers and solutions of generalized Bethe equations for an arbitray simply connected complex simple Lie group G. While in the simply laced case the resulting Bethe equations are the well-known Bethe equations for XXZ model, the non-simply laced cases feature different version of such equations which do not fit known XXZ models. Our results bring together several approaches to the q-deformed version of opers, namely older works on q-difference version Drinfeld-Sokolov reduction, paper by Mukhin and Varchenko on difference Miura opers and the recent approach of the speaker together with Sage and Zeitlin.