Twisted zastava and q-Whittaker functions

Abstract

Abstract. We implement the program outlined in [5, Section 7] extending to the case of non simply laced simple Lie algebras the construction of solutions of q-difference Toda equations from geometry of quasimaps' spaces. To this end we introduce and study the twisted zastava spaces.

Defects and quantum Seiberg-Witten geometry

“…In [62] the K-theoretic J-function of the flag variety was shown to be the (universal) eigenfunction of the relativistic Toda system for any simply laced group and in [63] the analysis was extended to non-simply laced groups.…”

Semi-infinite Plücker Relations and Weyl Modules

“…Our goal is to generalize the finite-dimensional picture to the semi-infinite settings [FiMi,BF1,BF2,Kat]. This means that the group G is replaced with the group G [[z]] and all the representations V are replaced with the infinite-dimensional spaces V [[z]] = V ⊗K [[z]].…”

“…Finally let us add a remark due to Michael Finkelberg. In the works [BF1,BF2,BF3], the authors study the rings of functions on zastava schemes (for the curve A 1 ) and the spaces of sections of line bundles over quasimaps' schemes (for the curve P 1 ); in particular, the characters of these spaces are computed. The results of this paper imply that these zastava and quasimaps as schemes representing the corresponding moduli problems, are non reduced (for G = SL(n), n ≥ 5).…”

“…The results of this paper imply that these zastava and quasimaps as schemes representing the corresponding moduli problems, are non reduced (for G = SL(n), n ≥ 5). The zastava and quasimaps' spaces studied in [BF1,BF2,BF3] are defined as the corresponding reduced schemes, i.e. varieties.…”

“…varieties. In particular, the character formulas of [BF1,BF2,BF3] hold for the spaces of sections over the reduced zastava and quasimaps' varieties.…”