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On parabolic Whittaker functions II

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Central European Journal of Mathematics

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We propose a Givental-type stationary phase integral representation for the restricted Gr m,N -Whittaker function, which is expected to describe the (S 1×U N )-equivariant Gromov-Witten invariants of the Grassmann variety Gr m,N . Our key tool is a generalization of the Whittaker model for principal series U(gl N )-modules, and its realization in the space of functions of totally positive unipotent matrices. In particular, our construction involves a representation theoretic derivation of the Batyrev-Ciocan-Fontanine-Kim-van Straten toric degeneration of Gr m,N .

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Correspondence to Sergey Oblezin.

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Oblezin, S. On parabolic Whittaker functions II. centr.eur.j.math. 10, 543–558 (2012). https://doi.org/10.2478/s11533-011-0129-5

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