Abstract In this paper, we generalize a result of Cuttler, Greene, Skandera, and Sra that characterizes the majorization order on Young diagrams in terms nonnegative specializations Schur polynomials. More precisely, introduce generalized notion associated to an arbitrary crystallographic root system $\Phi $ show it admits natural characterization values spherical functions any Riemannian symme...

A singular polynomial is one which is annihilated by all Dunkl operators for a certain parameter value. These polynomials were first studied by Dunkl, de Jeu and Opdam, (Trans. Amer. Math. Soc. 346 (1994), 237-256). This paper constructs a family of such polynomials associated to the irreducible representation (N − 2, 1, 1) of the symmetric group SN for odd N and parameter values − 1 2 ,− 3 2 ,...

The main result of this paper is a character sum identity for Cox-eter arrangements over nite elds which is an analogue of Macdonald's conjecture 19] proved by Opdam 21]. 0. Introduction Throughout this paper F will denote a nite eld of characteristic p diierent from 2. We rst slightly reformulate Macdonald's conjecture in a form which has a direct analogue over F. Let G be a nite subgroup of G...

The goal of this paper is to define a new class of objects which we call triple affine Artin groups and to relate them with Cherednik’s double affine Hecke algebras. This has as immediate consequences new and simple descriptions of double affine Weyl and Artin groups, the double affine Hecke algebras as well as the corresponding elliptic objects. We also recover in an transparent and elementary...

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We study a BGG-type category of infinite dimensional representations of H[W ], a semi-direct product of the quantum torus with parameter q, built on the root lattice of a semisimple group G, and the Weyl group of G. Irreducible objects of our category turn out to be parameterized by semistable G-bundles on the elliptic curve C/q. In the second part of the paper we construct a family of algebras...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

We study the polynomial representation of the rational Cherednik algebra of type An−1 with generic parameter in characteristic p for p | n. We give explicit formulas for generators for the maximal proper graded submodule, show that they cut out a complete intersection, and thus compute the Hilbert series of the irreducible quotient. Our methods are motivated by taking characteristic p analogues...