Related papers: Braid groups of normalizers of reflection subgroup…

We introduce a generalization of degenerate affine Hecke algebra, called wreath Hecke algebra, associated to an arbitrary finite group G. The simple modules of the wreath Hecke algebra and of its associated cyclotomic algebras are…

This paper and its sequel describe the irreducible representations of the rational Cherednik algebra $H_c(W)$ for a finite Coxeter group $W$ of type $H_4$, $F_4$ with equal parameters, $E_6$, $E_7$, and $E_8$, when $c$ is not a…

An affine Hecke algebra H contains a large abelian subalgebra A. The center Z of H is the subalgebra of Weyl group invariant elements in A. The natural trace of the affine Hecke algebra can be written as an integral of a rational $n$ form…

We define an imbedding of the Hecke algebra module carried by the involutions in a Weyl group W (defined by the author and Vogan) into a completion of the Hecke algebra. An analogous result is proved for any Coxeter group. A variant of the…

Let A be a \C-algebra with an action of a finite group G, let $\natural$ be a 2-cocycle on $G$ and consider the twisted crossed product $A \rtimes \C [G,\natural]$. We determine the Hochschild homology of $A \rtimes \C [G,\natural]$ for two…

Long and Moody gave a method of constructing representations of the braid group B_n. We discuss some ways to generalize their construction. One of these gives representations of subgroups of B_n, including the Gassner representation of the…

We consider normal subgroups $N$ of the braid group $B_n$ such that the quotient $B_n/N$ is an extension of the symmetric group by an abelian group. We show that, if $n\geq 4$, then there are exactly 8 commensurability classes of such…

Let $W$ be a finite Coxeter group. We give an algebraic presentation of what we refer to as ``the non-crossing algebra'', which is associated to the hyperplane complement of $W$ and to the cohomology of its Milnor fibre. This is used to…

This paper is a sequel to work of Dynkin on subroot lattices of root lattices and to work of Carter on presentations of Weyl group elements as products of reflections. The quotients $L/L_1$ are calculated for all irreducible root lattices…

Let $R$ be a root datum with affine Weyl group $W^e$, and let $H = H (R,q)$ be an affine Hecke algebra with positive, possibly unequal, parameters $q$. Then $H$ is a deformation of the group algebra $\mathbb C [W^e]$, so it is natural to…

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…

Heckenberger introduced the Weyl groupoid of a finite-dimensional Nichols algebra of diagonal type. We replace the matrix of its braiding by a higher tensor and present a construction which yields further Weyl groupoids. Abelian cohomology…

The descent algebra of a finite Coxeter group W is a subalgebra of the group algebra defined by Solomon. Descent algebras of symmetric groups have properties that are not shared by other Coxeter groups. For instance, the natural map from…

The BH algebra is defined by two sets of generators one of which satisfy the relations of the braid group and the other the relations of the Hecke algebra of projectors.These algebras are then combined by additional relations in a way which…

Let N be the normalizer of a maximal torus T in a split reductive group over F_q, and let w be an involution in the Weyl group N/T. We construct a section of W satisfying the braid relations, such that the image of the lift n of w under the…

Hopf algebroids are generalizations of Hopf algebras to less commutative settings. We show how the comultiplication defined by Kostant and Kumar turns the affine nil Hecke algebra associated to a Coxeter system into a Hopf algebroid without…

We study the action of the formal affine Hecke algebra on the formal group algebra, and show that the the formal affine Hecke algebra has a basis indexed by the Weyl group as a module over the formal group algebra. We also define a concept…

A type of directed multigraph called a W-digraph is introduced to model the structure of certain representations of Hecke algebras, including those constructed by Lusztig and Vogan from involutions in a Weyl group. Building on results of…

The structure of subring $J^{\Gamma \cap \Gamma^{-1}}$ of the asymptotic Hecke algebra is described for $\Gamma$ a left cell of the Coxeter group of type $H_4$. A small set of generators is produced. The subalgebras spanned by a subset of…

This article extends the works of Gon\c{c}alves, Guaschi, Ocampo [GGO] and Marin [MAR2] on finite subgroups of the quotients of generalized braid groups by the derived subgroup of their pure braid group. We get explicit criteria for…