Weyl modules and q-Whittaker functions
Abstract
Let G be a semi-simple simply connected group over complex numbers. In this paper we give a geometric definition of the (dual) Weyl modules over the group G[t] and show that their characters form an eigen-function of the lattice version of the q-Toda integrable integrable system (defined by means of the quantum group version of Kostant-Whittaker reduction due to Etingof and Sevostyanov). All the proofs are algebro-geometric and rely on our previous work which interprets the universal eigen-function of the q-Toda system in terms of rings of functions on the spaces of based quasi-maps from P^1 to the flag variety of G. We discuss in detail the relation between the current work and the works of Cherednik, Ion, Sanderson and Gerasimov-Lebedev-Oblezin.
Cite
@article{arxiv.1203.1583,
title = {Weyl modules and q-Whittaker functions},
author = {Alexander Braverman and Michael Finkelberg},
journal= {arXiv preprint arXiv:1203.1583},
year = {2017}
}
Comments
18 pages; v5: Lemmas 3,5, Proposition 4.3 corrected. v6: relations between various versions of definitions of quasimaps spaces and the formal arcs schemes (reduced or non-reduced) are clarified in Sections 2.2, 2.3