Zonal Polynomials And Quantum Antisymmetric Matrices
by Naihuan Jing   Robert Ray  

Vol. 7 No. 1 (2012) P.1~P.31

ABSTRACT

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.

KEYWORDS
Pfaffians, quantum groups, invariants, quantum anti-symmetric matrices

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 20G42, 17B37, 43A90, 05E10

MILESTONES

Received: 2011-09-26
Revised : 2011-10-06
Accepted: 2011-10-07

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