Multivariable generalizations of the classical Hermite, Laguerre and Jacobi polynomials occur as the polynomial part of the eigenfunctions of certain SchrÃ¶dinger operators forâ€¦ (More)

Abstract. We study multivariable (bilateral) basic hypergeometric series associated with (type A) Macdonald polynomials. We derive several transformation and summation properties for such series,â€¦ (More)

The theory of non-symmetric Jack polynomials is developed independently of the theory of symmetric Jack polynomials, and this theory together with the relationship between the non-symmetric,â€¦ (More)

For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic N j=1 x j âˆ’ x is computed exactly and shown to satisfy a central limitâ€¦ (More)

A q-analogue of the type A Dunkl operator and integral kernel We introduce the q-analogue of the type A Dunkl operators, which are a set of degreeâ€“lowering operators on the space of polynomials in nâ€¦ (More)

Averages of ratios of characteristic polynomials for the compact classical groups are evaluated in terms of determinants whose dimensions are independent of the matrix rank. These formulas are shownâ€¦ (More)

The SchrÃ¶dinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariableâ€¦ (More)

We investigate some properties of non-symmetric Jack, Hermite and Laguerre polynomials which occur as the polynomial part of the eigenfunctions for certain Calogero-Sutherland models with exchangeâ€¦ (More)