Whittaker vector of deformed Virasoro algebra and Macdonald symmetric functions
Quantum Algebra
2014-02-13 v1 High Energy Physics - Theory
Algebraic Geometry
Combinatorics
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.
Keywords
Cite
@article{arxiv.1402.2946,
title = {Whittaker vector of deformed Virasoro algebra and Macdonald symmetric functions},
author = {Shintarou Yanagida},
journal= {arXiv preprint arXiv:1402.2946},
year = {2014}
}