相关论文: Une formule de Plancherel pour l'alg`ebre de Hecke…
We determine a basis of the (twisted) cocenter of graded affine Hecke algebras with arbitrary parameters. In this setting, we prove that the kernel of the (twisted) trace map is the commutator subspace (Density theorem) and that the image…
Motivated by the Farrell-Jones Conjecture for group rings, we formulate the $\mathcal{C}$op-Farrell-Jones Conjecture for the K-theory of Hecke algebras of td-groups. We prove this conjecture for (closed subgroups of) reductive p-adic groups…
We describe algorithms to represent and compute groups of Hecke characters. We make use of an id{\`e}lic point of view and obtain the whole family of such characters, including transcendental ones. We also show how to isolate the algebraic…
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…
The quantum dynamical Yang-Baxter (or Gervais-Neveu-Felder) equation defines an R-matrix R(p), where $p$ stands for a set of mutually commuting variables. A family of SL(n)-type solutions of this equation provides a new realization of the…
The paper studies weak Paley-Wiener properties for group extensions by use of Mackey's theory. The main theorem establishes sufficient conditions on the dual action to ensure that the group has the weak Paley-Wiener property. The theorem…
We prove that the affine Yokonuma-Hecke algebra defined by Chlouveraki and Poulain d'Andecy is a particular case of the pro-$p$-Iwahori-Hecke algebra defined by Vign\'eras.
Let $W$ be a finite Weyl group of classical type which may not be irreducible, $F$ an algebraically closed field, $q$ an invertible element of $F$. We denote by $\mathcal H_W(q)$ the associated Hecke algebra. If $q=1$ then it is $FW$ and we…
We formulate a Satake isomorphism for the integral spherical Hecke algebra of an unramified $p$-adic group $G$ and generalize the formulation to give a description of the Hecke algebra $H_G(V)$ of weight $V$, where $V$ is a lattice in an…
We give an explicit expression for the central elements of affine Hecke algebras of type A in the Coxeter presentation, in terms of (parabolic) affine Kazhdan-Lusztig polynomials. Our approach is based on a version of quantum affine…
In this paper it is shown that a quantum observable algebra, the Heisenberg-Weyl algebra, is just given as the Hopf algebraic dual to the classical observable algebra over classical phase space and the Plank constant is included in this…
Lusztig proved that the Kazhdan-Lusztig basis of a spherical Hecke algebra can be essentially identified with the Weyl characters of the Langlands dual group. We generalize this result to the unequal parameter case. The new proof is pretty…
The subalgebra of diagonal elements of a quantum matrix group has been conjectured by Daniel Krob and Jean-Yves Thibon to be isomorphic to a cubic algebra, coined the quantum pseudo-plactic algebra. We present a functorial approach to the…
Associated to the classical Weyl groups, we introduce the notion of degenerate spin affine Hecke algebras and affine Hecke-Clifford algebras. For these algebras, we establish the PBW properties, formulate the intertwiners, and describe the…
We show that the category O for a rational Cherednik algebra of type A is equivalent to modules over a q-Schur algebra (parameter not a half integer), providing thus character formulas for simple modules. We give some generalization to…
We construct a bijection between certain Deodhar components of a braid variety constructed from an affine Kac-Moody group of type $A_{n-1}$ and vertex-labeled trees on $n$ vertices. By an argument of Galashin, Lam, and Williams using…
For a Weyl group W, we give a simple closed formula (valid on elliptic conjugacy classes) for the character of the representation of W in each A-isotypic component of the full homology of a Springer fiber. We also give a formula (valid…
Let W be a finite Coxeter group. We define its Hecke-group algebra by gluing together appropriately its group algebra and its 0-Hecke algebra. We describe in detail this algebra (dimension, several bases, conjectural presentation,…
We review the construction of generalized affine Hecke algebras attached to Bernstein series of both smooth irreducible and enhanced $L$-parameters of $p$-adic reductive groups and apply it to the study of the Howe correspondence.
This paper constructs a representation of a Hecke algebra on a vector space spanned by the involutions in a Coxeter group.