On parabolic Whittaker functions II

Details On parabolic Whittaker functions II On parabolic Whittaker functions II

2011-07-15

arxiv.org/abs/1107.2998v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

We derive a Givental-type stationary phase integral representation for the specified $\Gr_{m,N}$-Whittaker function introduced in \cite{GLO2}, which presumably describes the $S^1\times U_N$-equivariant Gromov-Witten invariants of Grassmann variety $\Gr_{m,N}$. Our main tool is a generalization of Whittaker model for principal series $\CU(\frak{gl}_N)$-modules. In particular, our construction includes a representation theory interpretation of the Batyrev--Ciocan-Fontanine--Kim--van Straten toric degeneration of Grassmannian, providing a direct connection between this toric degeneration of $\Gr_{m,N}$ and total positivity for unipotent matrices.

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