Quantum Deformation of the W_N Algebra
H. Awata, H. Kubo, S. Odake, J. Shiraishi
TL;DR
This paper reviews the quantum deformation of the W_N algebra, highlighting its construction via free fields and Miura transformation, and its connection to Jack and Macdonald polynomials.
Contribution
It provides a comprehensive review of the quantum deformed W_N algebra, emphasizing its realization through free fields and its relation to special polynomials.
Findings
Quantum deformed W_N algebra defined via Miura transformation
Singular vectors correspond to Jack and Macdonald polynomials
Framework applicable to extended and quantum algebra applications
Abstract
We review the W_N algebra and its quantum deformation, based on free field realizations. The (quantum deformed) W_N algebra is defined through the (quantum deformed) Miura transformation, and its singular vectors realize the Jack (Macdonald) polynomials. (Talk at the Nankai-CRM joint meeting on ``Extended and Quantum Algebras and their Applications to Physics'', Tianjin, China, August 19-24, 1996.)
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons