Related papers: On tensor categories attached to cells in affine W…
This paper makes precise the close connection between the affine Hecke algebra, the path model, and the theory of crystals. Section 2 is a basic pictorial exposition of Weyl groups and affine Weyl groups and Section 5 is an exposition of…
We study the intermediate extension of the character sheaves on an adjoint group to the semi-stable locus of its wonderful compactification. We show that the intermediate extension can be described by a direct image construction. As a…
Let H = H (R,q) be an affine Hecke algebra with complex, possibly unequal parameters q, which are not roots of unity. We compute the Hochschild and the cyclic homology of H. It turns out that these are independent of q and that they admit…
We prove that the category of finitely generated graded modules over the quiver Hecke algebra of arbitrary type admits numerous stratifications in the sense of Kleshchev. A direct consequence is that the full subcategory corresponding to…
By Tits' deformation argument, a generic Iwahori--Hecke algebra $H$ associated to a finite Coxeter group $W$ is abstractly isomorphic to the group algebra of $W$. Lusztig has shown how one can construct an explicit isomorphism, provided…
The goal of this paper is to define a new class of objects which we call triple groups and to relate them with Cherednik's double affine Hecke algebras. This has as immediate consequences new descriptions of double affine Weyl and Artin…
This paper contains a complete description of minimal non-gatherable triangle triples in the lambda-sequences for the affine classical root systems and some claims for arbitrary (reduced) affine root systems. It continues our previous paper…
Let G be a reductive group over an algebraically closed field k of very good characteristic. The Lusztig-Vogan bijection is a bijection between the set of dominant weights for G and the set of irreducible G-equivariant vector bundles on…
We construct a model of the affine nil-Hecke algebra as a subalgebra of the Nichols-Woronowicz algebra associated to a Yetter-Drinfeld module over the affine Weyl group. We also discuss the Peterson isomorphism between the homology of the…
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…
To any element of a connected, simply connected, semisimple complex algebraic group G and a choice of an element of the corresponding Weyl group there is an associated Lusztig variety. When the element of G is regular semisimple, the…
We compare the (horizontal) trace of the affine Hecke category with the elliptic Hall algebra, thus obtaining an "affine" version of the construction of [14]. Explicitly, we show that the aforementioned trace is generated by the objects…
In the previous paper "Symmetric Crystals and Affine Hecke Algebras of Type B", we formulated a conjecture on the relations between certain classes of irreducible representations of affine Hecke algebras of type B and symmetric crystals for…
This paper presents categorifications of (right) cell modules and induced cell modules for Hecke algebras of finite Weyl groups. In type $A$ we show that these categorifications depend only on the isomorphism class of the cell module, not…
We are interested in cell properties of translations in affine Weyl groups. We find out some translations in the second lowest two-sided cell of an affine Weyl group and use the translations to formulate a refinement of Jianyi Shi's…
We introduce a new language to describe the geometry of affine Deligne-Lusztig varieties in affine flag varieties. This second part of a two paper series uses this new language, i.e. the double Bruhat graph, to describe certain structure…
We develop abstract nonsense for module categories over monoidal categories (this is a straightforward categorification of modules over rings). As applications we show that any semisimple monoidal category with finitely many simple objects…
Let $(W,S)$ be a Coxeter system, let $G$ be a finite solvable group of automorphisms of $(W,S)$ and let $\varphi$ be a weight function which is invariant under $G$. Let $\varphi_G$ denote the weight function on $W^G$ obtained by restriction…
Let $k$ be an algebraically closed field of characteristic $p\ge 0$. Let $G$ be an affine group scheme over $k$. We classify the indecomposable exact module categories over the rigid tensor category $\text{Coh}_f(G)$ of coherent sheaves of…
We incorporate a category of certain modules for an affine Lie algebra, of a certain fixed non-positive-integral level, considered by Kazhdan and Lusztig, into the representation theory of vertex operator algebras, by using the logarithmic…