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

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

1995-03-27

arxiv.org/abs/math/9503224v1

Mathematics

Quantum Algebra

Scientific paper

Quantum analogues of the homogeneous spaces $\GL(n)/\SO(n)$ and
$\GL(2n)/\Sp(2n)$ are introduced. The zonal spherical functions on these
quantum homogeneous spaces are represented by Macdonald's symmetric
polynomials $P_{\ld}=P_{\ld}(x_1,\cdots,x_n;q,t)$ with $t=q^{1 \over 2}$ or
$t=q^2$.

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