On q-deformed gl(l+1)-Whittaker function

Details On q-deformed gl(l+1)-Whittaker function On q-deformed gl(l+1)-Whittaker function

2008-03-02

arxiv.org/abs/0803.0145v1

Mathematics

Representation Theory

20 pages

Scientific paper

We propose new explicit form of q-deformed Whittaker functions solving q-deformed gl(l+1)-Toda chains. In the limit q->1 constructed solutions reduce to classical class one gl(l+1)-Whittaker functions in the form proposed by Givental. An important property of the proposed expression for the q-deformed gl(l+1)-Whittaker function is that it can be represented as a character of C*x GL(l+1). This provides a q-version of the Shintani-Casselman-Shalika formula for p-adic Whittaker function. The Shintani-Casselman-Shalika formula is recovered in the limit q->0 when the q-deformed Whittaker function is reduced to a character of a finite-dimensional representation of gl(l+1) expressed through Gelfand-Zetlin bases.

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