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Nonsymmetric Koornwinder polynomials and duality
Siddhartha Sahi
Motivated by the work of Koornwinder, Macdonald, Cherednik, Noumi, and van Diejen we define a 6-parameter double affine Hecke algebra and establish its basic structural properties,…
The binomial formula for nonsymmetric Macdonald polynomials
Siddhartha Sahi
Inhomogeneous analogues of symmetric and nonsymmetric Macdonald polynomials were introduced by F. Knop and the author. In the symmetric case A. Okounkov has recently proved a beaut…
Difference equations and symmetric polynomials defined by their zeros
Friedrich Knop, Siddhartha Sahi
In this paper, we introduce a new family of symmetric polynomials which depends on a parameter r. They are defined by specifying certain of their zeros. For the parameter values 1/…
A recursion and a combinatorial formula for Jack polynomials
Friedrich Knop, Siddhartha Sahi
Heckman and Opdam introduced a non-symmetric analogue of Jack polynomials using Cherednik operators. In this paper, we derive a simple recursion formula for these polynomials and f…
A new scalar product for nonsymmetric Jack polynomials
Siddhartha Sahi
Symmetric Jack polynomials arise naturally in several contexts, including statistics, physics, combinatorics, and representation theory. They are pairwise orthogonal with repsect t…