Level-0 action of U_q(sl_n) on the q-deformed Fock spaces

1996/07/30 by Kouichi Takemura, Takemura, Kouichi, Denis Uglov +1
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9607031

24 pages, AMSLaTex

arxiv created 1996/07/30 · arxiv updated 2009/11/30

Abstract

On the level-1 Fock space modules of the algebra U_q(sl_n) we define a level-0 action U₀ of the U_q(sl_n), and an action of an abelian algebra of conserved Hamiltonians commuting with the U₀. An irreducible decomposition of the Fock space with respect to the level-0 action is derived by constructing a base of the Fock space in terms of the Non-symmetric Macdonald Polynomials.

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• New Level-0 Action of U_q(\widehatsl₂) on Level-1 Modules
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