On a classical limit of q-deformed Whittaker functions

TL;DR

This paper derives the classical $gl_{ ext{ell+1}}$-Whittaker function as a limit of its q-deformed version, connecting quantum and classical representations through Gelfand-Zetlin patterns.

Contribution

It provides a new derivation of the Givental integral representation from the q-deformed functions in the classical limit.

Findings

Established the limit $q o 1$ connecting q-deformed and classical Whittaker functions.

Expressed the classical Whittaker function as a Givental integral.

Linked quantum and classical representations via Gelfand-Zetlin patterns.

Abstract

We provide a derivation of the Givental integral representation of the classical $gl_{\ell+1}$-Whittaker function as a limit $q \to 1$ of the q-deformed $gl_{\ell+1}$-Whittaker function represented as a sum over the Gelfand-Zetlin patterns.