2012/03/31 by Alexander Braverman, Michael Finkelberg · 1 citation
Mathematics · #math.RT #math.AG #math.CO #math.QA
published as Math. Ann. 359 (2014), no.1-2, 45--59 · 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
arxiv created 2017/12/03 · arxiv updated 2017/12/05
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 P1 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.