Gelfand pairs and spherical functions.
Generalisations of some properties of invariant polynomials with matrix arguments
Some extensions of the properties of invariant polynomials proved by Davis (1980), Chikuse (1980), Chikuse and Davis (1986) and Ratnarajah et al. (2005) are given for symmetric and Hermitian matrices.
Generalizations of Milne’s -Chu-Vandermonde summation
We derive two identities for multiple basic hyper-geometric series associated with the unitary group. In order to get the two identities, we first present two known -exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two -Chu-Vandermonde summations established by Milne, we arrive at our...
Generalized Jacobi polynomials and Selberg integrals. (Polynômes de Jacobi généralisés et intégrales de Selberg.)
Generalized Picard lattices arising from half-integral conditions
Generating functions on extended Jacobi polynomials from Lie group view point.
Generating functions play a large role in the study of special functions. The present paper deals with the derivation of some novel generating functions of extended Jacobi polynomials by the application of [the] group-theoretic method introduced by Louis Weisner. In fact, by suitably interpreting the index (n) and the parameter (β) of the polynomial under consideration we define four linear partial differential operators and on showing that they generate a Lie-algebra, we obtain a new generating...
Geometric structures on the complement of a projective arrangement
Consider a complex projective space with its Fubini-Study metric. We study certain one parameter deformations of this metric on the complement of an arrangement (= finite union of hyperplanes) whose Levi-Civita connection is of Dunkl type. Interesting examples are obtained from the arrangements defined by finite complex reflection groups. We determine a parameter interval for which the metric is locally of Fubini-Study type, flat, or complex-hyperbolic. We find a finite subset of this interval for...