Whittaker vector of deformed Virasoro algebra and Macdonald symmetric functions

2014/02/12 by Shintarou Yanagida, Yanagida, Shintarou · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1402.2946

openalex publication_date 2014/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a proof of Awata and Yamada's conjecture for the explicit formula of Whittaker vector of the deformed Virasoro algebra realized in the Fock space. The formula is expressed as a summation over Macdonald symmetric functions with factored coefficients. In the proof we fully use currents appearing in the Fock representation of Ding-Iohara-Miki quantum algebra. We also mention an interpretation of Whittaker vector in terms of the geometry of the Hilbert schemes of points on the affine plane.

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