Noncommutative analogues of q-special polynomials and q-integral on a quantum sphere

Details Noncommutative analogues of q-special polynomials and q-integral on a quantum sphere Noncommutative analogues of q-special polynomials and q-integral on a quantum sphere

1997-12-02

arxiv.org/abs/q-alg/9712008v1

Mathematics

Quantum Algebra

14 pages Latex

Scientific paper

10.1088/0305-4470/31/7/011

The q-Legendre polynomials can be treated as some special "functions in the quantum double cosets $U(1)\setminus SU_q(2)/U(1)$". They form a family (depending on a parameter $q$) of polynomials in one variable. We get their further generalization by introducing a two parameter family of polynomials. If the former family arises from an algebra which is in a sense "q-commutative", the latter one is related to its noncommutative counterpart. We introduce also a two parameter deformation of the invariant integral on a sphere.

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