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

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.

revised, 22 pages

References in corpus (3)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Asymptotically free N=2 theories and irregular conformal blocks
• Instanton counting via affine Lie algebras I: Equivariant J-functions of (affine) flag manifolds and Whittaker vectors

Cited by in corpus (14)

• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• A direct proof of AGT conjecture at beta = 1
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Notes on Ding-Iohara algebra and AGT conjecture
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• A slow review of the AGT correspondence
• Quantum toroidal algebras and solvable structures in gauge/string theory
• On the Jeffrey-Kirwan residue of BCD-instantons
• AFLT-type Selberg integrals
• Conformal blocks and Painlevé functions
• Whittaker modules for a subalgebra of N=2 superconformal algebra
• $U(\fh)$-free modules over the Block algebra $\BB(q)$
• Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)
• Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of 5D AGT Conjecture