Moscow Mathematical Journal

Volume 17, Issue 4, October–December 2017 pp. 565–600.

Quasimap Counts and Bethe Eigenfunctions

Authors: Mina Aganagic (1) and Andrei Okounkov (2)
Author institution:(1) Center for Theoretical Physics, University of California, Berkeley, CA 94720, U.S.A and Department of Mathematics, University of California, Berkeley, CA 94720, U.S.A
(2) Department of Mathematics, Columbia University, New York, NY 10027, U.S.A.; Institute for Problems of Information Transmission, Bolshoy Karetny 19, Moscow 127994, Russia, and Laboratory of Representation, Theory and Mathematical Physics, Higher School of Economics, Myasnitskaya 20, Moscow 101000, Russia

Summary:

We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties. This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik–Zamolodchikov and dynamical q-difference equations.

2010 Math. Subj. Class. 82B23, 14N35.

Keywords: Quasimaps, Bethe ansatz, Knizhnik–Zamolodchikov equations.

Contents Full-Text PDF