Macdonald's symmetric polynomials as zonal spherical functions on some\n quantum homogeneous spaces

1995/03/26 by Masatoshi Noumi, Noumi, Masatoshi · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.math/9503224

Abstract

Quantum analogues of the homogeneous spaces GL(n)/ SO(n) and\n GL(2n)/ Sp(2n) are introduced. The zonal spherical functions on these\nquantum homogeneous spaces are represented by Macdonald's symmetric polynomials\nP _ld=P _ld(x₁,\⋯,x_n;q,t) with t=q^{1 over 2} or t=q².\n

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• Freidel-Maillet type equations on fused K-matrices over the positive part of U_q(\widehat\mathfraksl₂)
• q-deformed Howe duality for orthosymplectic Lie superalgebras
• 2-Homogeneous bipartite distance-regular graphs and the quantum group U^′_q(\mathfrakso₆)

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