Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial

TL;DR

This paper provides explicit formulas for Whittaker vectors of the Virasoro algebra using Jack symmetric polynomials, leveraging bosonization and Calogero-Sutherland model techniques.

Contribution

It introduces a novel explicit expression for Virasoro Whittaker vectors in terms of Jack polynomials, connecting algebraic and integrable model methods.

Findings

Explicit formulas for Whittaker vectors derived

Connections established between Virasoro algebra and Jack polynomials

Utilizes bosonization and Calogero-Sutherland model techniques

Abstract

We give explicit formulae of Whittaker vectors for Virasoro algebra in terms of the Jack symmetric polynomials. Our fundamental tools are the Feigin-Fuchs bosonization and the split expression of the Calogero-Sutherland model given by Awata-Matsuo-Odake-Shiraishi.