Zonal Polynomials and Quantum Antisymmetric Matrices

Details Zonal Polynomials and Quantum Antisymmetric Matrices Zonal Polynomials and Quantum Antisymmetric Matrices

2011-09-16

arxiv.org/abs/1109.3567v1

Bull. Inst. Math. Acad. Sinica (New Ser.) 7 (2012), 1-31

Mathematics

Representation Theory

Scientific paper

We study the quantum symmetric spaces for quantum general linear groups modulo symplectic groups. We first determine the structure of the quotient quantum group and completely determine the quantum invariants. We then derive the characteristic property for quantum Phaffian as well as its role in the quantum invariant sub-ring. The spherical functions, viewed as Macdonald polynomials, are also studied as the quantum analog of zonal spherical polynomials.

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