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arXiv · 1402.2946

Whittaker vector of deformed Virasoro algebra and Macdonald symmetric functions

Shintarou Yanagida
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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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BibTeXRIS

Shintarou Yanagida. 2014-02-12. Whittaker vector of deformed Virasoro algebra and Macdonald symmetric functions. https://arxiv.org/abs/1402.2946

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