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Finite difference quantum Toda lattice via equivariant K-theory

Alexander Braverman·Michael Finkelberg
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Abstract

We construct the action of the quantum group U_v(sl_n) by the natural correspondences in the equivariant localized $K$-theory of the Laumon based Quasiflags' moduli spaces. The resulting module is the universal Verma module. We construct geometrically the Shapovalov scalar product and the Whittaker vectors. It follows that a certain generating function of the characters of the global sections of the structure sheaves of the Laumon moduli spaces satisfies a $v$-difference analogue of the quantum Toda lattice system, reproving the main theorem of Givental-Lee. The similar constructions are performed for the affine Lie agebra \hat{sl}_n.

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Alexander Braverman, Michael Finkelberg. 2014-05-27. Finite difference quantum Toda lattice via equivariant K-theory. https://doi.org/10.1007/s00031-005-0402-4

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