Related papers: Hecke algebras and symplectic reflection algebras
We begin the study of unitary representations of Hecke algebras of complex reflections groups. We obtain a complete classification for the Hecke algebra of the symmetric group $\mathfrak{S}_n$ over the complex numbers. Interestingly, the…
These notes are based on a course given at the EPFL in May 2005. It is concerned with the representation theory of Hecke algebras in the non-semisimple case. We explain the role that these algebras play in the modular representation theory…
The goal of this paper is to present some results and (more importantly) state a number of conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products categorifies certain structures in the…
We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…
In this note we are interested in labelling the irreducible representations of non-semisimple specialisations of Hecke algebras of complex reflection groups. We will use category O for the rational Cherednik algebra and the KZ functor…
We investigate deformations of skew group algebras arising from the action of the symmetric group on polynomial rings over fields of arbitrary characteristic. Over the real or complex numbers, Lusztig's graded affine Hecke algebra and…
Ginzburg, Guay, Opdam and Rouquier established an equivalence of categories between a quotient category of the category $\mathcal{O}$ for the rational Cherednik algebra and the category of finite dimension modules of the Hecke algebra of a…
Basic properties of symplectic reflection algebras over an algebraically closed field k of positive characteristic are laid out. These algebras are always finite modules over their centres, in contrast to the situation in characteristic 0.…
We investigate the extensions of the Hecke algebras of finite (complex) reflection groups by lattices of reflection subgroups that we introduced, for some of them, in our previous work on the Yokonuma-Hecke algebras and their connections…
In this paper we define a two-variable, generic Hecke algebra, H, for each complex reflection group G(b,1,n). The algebra H specializes to the group algebra of G(b,1,n) and also to an endomorphism algebra of a representation of GL(n,q)…
Let $\cH$ be the one-parameter Hecke algebra associated to a finite Weyl group $W$, defined over a ground ring in which ``bad'' primes for $W$ are invertible. Using deep properties of the Kazhdan--Lusztig basis of $\cH$ and Lusztig's…
From the combinatorial characterizations of the right, left, and two-sided Kazhdan-Lusztig cells of the symmetric group, 'RSK bases' are constructed for certain quotients by two-sided ideals of the group ring and the Hecke algebra.…
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…
In this paper we study the Hecke algebra associated with a complex reflection group W. We discuss some properties of the Galois group of the splitting field of this algebra, and study its action on the so-called fake degrees of W. The…
We give an overview of the representation theory of restricted rational Cherednik algebras. These are certain finite-dimensional quotients of rational Cherednik algebras at t=0. Their representation theory is connected to the geometry of…
Symplectic reflection algebras arise in many different mathematical disciplines: integrable systems, Lie theory, representation theory, differential operators, symplectic geometry. In this paper, we introduce baby Verma modules for…
With an eye to applications to type A and Schur-Weyl duality, we study Kazhdan-Lusztig bases for a general parabolic Hecke algebra. Parabolic Hecke algebras are idempotent subalgebras of Hecke algebras corresponding to parabolic subgroups,…
We describe a positive characteristic analogue of the Kazhdan-Lusztig basis of the Hecke algebra of a crystallographic Coxeter system and investigate some of its properties. Using Soergel calculus we describe an algorithm to calculate this…
Graded Hecke algebras can be constructed in terms of equivariant cohomology and constructible sheaves on nilpotent cones. In earlier work, their standard modules and their irreducible modules where realized with such geometric methods. We…
We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, spaces of representations of quivers, and on…