Quantum $W_N$ Algebras and Macdonald Polynomials

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H. Awata , H. Kubo , S. Odake , J. Shiraishi This is my paper

classification q-alg hep-thmath.QA

keywords quantummacdonaldpolynomialsalgebraalgebrasdeformationderivemiura

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We derive a quantum deformation of the $W_N$ algebra and its quantum Miura transformation, whose singular vectors realize the Macdonald polynomials.

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Proves uniqueness of solutions to constraints on (q,t)-deformed hypergeometric functions and derives superintegrability relations for a general (q,t)-deformed matrix model with allowed parameters.