Finite difference quantum Toda lattice via equivariant K-theory

Alexander Braverman, Michael Finkelberg

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


We construct the action of the quantum group Uv(sln) 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 and Lee (cf.[7]). Similar constructions are performed for the affine Lie algebra sln.

Original languageEnglish
Pages (from-to)363-386
Number of pages24
JournalTransformation Groups
Issue number3-4
Publication statusPublished - Dec 2005
Externally publishedYes


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