Related papers: Hecke Modules from Metaplectic Ice
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…
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…
Cocenters of Hecke algebras $\mathcal H$ play an important role in studying mod $\ell$ or $\mathbb C$ harmonic analysis on connected $p$-adic reductive groups. On the other hand, the depth $r$ Hecke algebra $\mathcal H_{r^+}$ is well suited…
In this paper, we construct a representation of loop group and derive the formula of the corresponding representation of the affine Kac-Moody algebra with level 1. And we also provide a concrete realization of Whittaker functionals in the…
Let $W$ be an affine Weyl group, and let $\Bbbk$ be a field of characteristic $p>0$. The diagrammatic Hecke category $\mathcal{D}$ for $W$ over $\Bbbk$ is a categorification of the Hecke algebra for $W$ with rich connections to modular…
In this paper we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type $A_n$ to the category of finite-dimensional modules of the graded affine Hecke algebra of type $A_\ell$.…
The usual combinatorial model for the 0-Hecke algebra of the symmetric group is to consider the algebra (or monoid) generated by the bubble sort operators. This construction generalizes to any finite Coxeter group W. The authors previously…
We construct, for any symplectic, unitary or special orthogonal group over a locally compact nonarchimedean local field of odd residual characteristic, a type for each Bernstein component of the category of smooth representations, using…
We introduce the spin Hecke algebra, which is a q-deformation of the spin symmetric group algebra, and its affine generalization. We establish an algebra isomorphism which relates our spin (affine) Hecke algebras to the (affine)…
In this paper we compute new values of Iwahori Whittaker functions on $n$-fold metaplectic covers $\widetilde{G}$ of $\mathbf{G}(F)$ with $\mathbf{G}$ a split reductive group over a non-archimedean local field $F$. For every Iwahori…
Hecke symmetries generalize the usual tensor symmetry of vector spaces $v\otimes w\arrow w\otimes v$ as well as the symmetry of vector superspaces. To a Hecke symmetry $R$ there associates a quadratic algebra which can be interpreted as the…
We describe an algorithm for computing the $p$-canonical basis of the Hecke algebra, or one of its antispherical modules. The algorithm does not operate in the Hecke category directly, but rather uses a faithful embedding of the Hecke…
We consider finite groups acting on quantum (or skew) polynomial rings. Deformations of the semidirect product of the quantum polynomial ring with the acting group extend symplectic reflection algebras and graded Hecke algebras to the…
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…
In this paper we extend the results in [Ra] on the representation of the Hecke algebra, determined by the matrix coefficients of a projective, unitary representation, in the discrete series of representations of the ambient group, to a more…
We review some facts about the representation theory of the Hecke algebra. We adapt for the Hecke algebra case the approach of Okounkov and Vershik which was developed for the representation theory of symmetric groups. We justify an…
We relate the classes of unitary and calibrated representations of cyclotomic Hecke algebras and, in particular, we show that for the most important deformation parameters these two classes coincide. We classify these representations in…
We use techniques from statistical mechanics to provide new formulas for Whittaker coefficients of metaplectic Eisenstein series on odd orthogonal groups, matching Friedberg and Zhang. We study a particular variation/generalization of the…
We will give new applications of quantum groups to the study of spherical Whittaker functions on the metaplectic $n$-fold cover of $GL(r,F)$, where $F$ is a nonarchimedean local field. Earlier Brubaker, Bump, Friedberg, Chinta and Gunnells…
Recently Delorme and Opdam have generalized the theory of R-groups towards affine Hecke algebras with unequal labels. We apply their results in the case where the affine Hecke algebra is of type B, for an induced discrete series…