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.

arXiv commentrevised, 22 pages

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• 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
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• Whittaker modules for the affine Lie algebra $A_1^{(1)}$
• Notes on Ding-Iohara algebra and AGT conjecture
• Towards a proof of AGT conjecture by methods of matrix models
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• A slow review of the AGT correspondence
• Whittaker pairs for the Virasoro algebra and the Gaiotto - BMT states
• Irregular conformal blocks, with an application to the fifth and fourth Painlevé equations
• Superconformal field theory and Jack superpolynomials
• Quantum toroidal algebras and solvable structures in gauge/string theory
• A family of simple weight modules over the Virasoro algebra
• On the Jeffrey-Kirwan residue of BCD-instantons
• Classical limit of irregular blocks and Mathieu functions
• Irreducible Virasoro modules from irreducible Weyl modules
• AFLT-type Selberg integrals
• Conformal blocks and Painlevé functions
• Jack vertex operators and realization of Jack functions
• Notes on 3-point functions of A_{N-1} Toda theory and AGT-W relation for SU(N) quiver
• Simple Virasoro modules which are locally finite over a positive part
• Whittaker modules for a subalgebra of N=2 superconformal algebra
• $U(\fh)$-free modules over the Block algebra $\BB(q)$
• A class of simple weight Virasoro modules
• Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)
• Super-Whittaker vector at c=3/2
• Simple restricted modules for Neveu-Schwarz algebra
• Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of 5D AGT Conjecture
• Generalized Polynomial modules over the Virasoro algebra
• Whittaker modules for the super-Virasoro algebras