Related papers: Class polynomials for some affine Hecke algebras
This is an extended and corrected version of the author's Diplomarbeit. A class of algebras called generic pro-$p$ Hecke algebras is introduced, enlarging the class of generic Hecke algebras by considering certain extensions of (extended)…
This is a survey paper about affine Hecke algebras. We start from scratch and discuss some algebraic aspects of their representation theory, referring to the literature for proofs. We aim in particular at the classification of irreducible…
We study a class of representations called ``calibrated representations'' of the degenerate double affine Hecke algebra and those of the rational Cherednik algebra of type ${\mathrm{GL}}_n$. We give a realization of calibrated irreducible…
We give a $K$-theoretic realization of all affine Hecke algebras with two unequal parameters including exceptional types. This extends the celebrated work of Kazhdan and Lusztig, who gave a $K$-theoretic realization of affine Hecke algebras…
Let F be a finite group and X be a complex quasi-projective F-variety. For r in N, we consider the mixed Hodge-Deligne polynomials of quotients X^r/F, where F acts diagonally, and compute them for certain classes of varieties X with simple…
The affine Hecke algebra $\dot H_n$ of type $A$ is often presented as a quotient of the braid algebra of $n$-braids in the annulus. This leads to diagrammatic representations in terms of braids in the annulus, subject to a quadratic…
We show that affine Hecke algebras of rank two with generic parameters are affine cellular in the sense of Koenig-Xi.
Affine Lusztig varieties encode the orbital integrals of Iwahori--Hecke functions and serve as building blocks for the (conjectural) theory of affine character sheaves. We establish a close relationship between affine Lusztig varieties and…
We introduce a class of induced representations of the degenerate double affine Hecke algebra of gl_N and analyze their structure mainly by means of intertwiners. We also construct them from modules of the affine Lie algebra using…
In this paper we consider the Hecke algebra $\mathcal {H}$ associated to an extended affine Weyl group of type $\widetilde{B_2}$. We give some interesting formulas on $C_{rt}S_{\lambda}$, which imply some relations between the…
Let $G$ be a semisimple simply-connected algebraic group over an algebraically closed field of characteristic zero. We prove that the affine Hecke category associated to the loop group of $G$ is equivalent to the colimit, evaluated in the…
We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra H of GL. These functors…
A class of generalized complex polynomials of Hermite type, suggested by a special magnetic Schrodinger operator, is introduced and some related basic properties are discussed.
We establish a q-generalization of Gordon's theorem that the space of diagonal coinvariants has a quotient identified with a perfect representation of the rational double affine Hecke algebra. It leads to a simple proof of his theorem and…
We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra.…
We describe a categorification of the Double Affine Hecke Algebra (${\mathcal{H}\kern -.4em\mathcal{H}}$) associated with an affine Lie algebra $\widehat{\mathfrak{g}}$, including a categorification of the polynomial representation and…
We define and study two new classes of algebras, called higher-level affine wreath product algebras and higher-level affine Frobenius Hecke algebras. They depend on a Frobenius superalgebra and are defined, respectively, as path algebras of…
We consider four classes of classical groups over a non-archimedean local field F: symplectic, (special) orthogonal, general (s)pin and unitary. These groups need not be quasi-split over F. The main goal of the paper is to obtain a local…
We study the structure and representation theory of affine wreath product algebras and their cyclotomic quotients. These algebras, which appear naturally in Heisenberg categorification, simultaneously unify and generalize many important…
We consider two families of polynomials that play the same role in the Temperley Lieb algebra of a Coxeter group as the Kazhdan Lusztig and R polynomials play in the Hecke algebra of the group. We study these polynomials from a…