Related papers: A note on Integral Satake isomorphisms

We characterize the space of new forms for $\Gamma_0(m)$ as a common eigenspace of certain Hecke operators which depend on primes $p$ dividing the level $m$. To do that we find generators and relations for a $p$-adic Hecke algebra of…

We study the representation theory of a generalized graded Hecke algebra associated to a complex reflection group of type G(r,1,n), defined by Ram and Shepler. We use a realization of this algebra in the corresponding symplectic reflection…

For an almost split Kac-Moody group G over a local non-archimedean field, the last two authors constructed a spherical Hecke algebra H (over the complex numbers C, say) and its Satake isomorphism with the commutative algebra of Weyl…

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…

Given an arbitrary graph $E$ we investigate the relationship between $E$ and the groupoid $G_E$. We show that there is a lattice isomorphism between the lattice of pairs $(H, S)$, where $H$ is a hereditary and saturated set of vertices and…

For a Hecke pair $(G, H)$ and a finite-dimensional representation $\sigma$ of $H$ on $V_\sigma$ with finite range we consider a generalised Hecke algebra $\H_\sigma(G, H)$, which we study by embedding the given Hecke pair in a Schlichting…

Let $G$ be a reductive $p$--adic group. Assume that $L\subset G$ is an open--compact subgroup, and $\mathcal H_L$ is the Hecke algebra of $L$--biinivariant complex functions on $G$. It is a well--known and standard result on how to prove…

Let H be a Hecke algebra arising as an endomorphism algebra of the representation of a Chevalley group G over F_q induced by a unipotent cuspidal representation of a Levi quotient L of a parabolic subgroup. We assume that L is not a torus.…

Let $G$ be a linear connected non-compact real simple Lie group and let $K\subset G$ be a maximal compact subgroup of $G$. Suppose that the centre of $K$ isomorphic to $\mathbb{S}^1$ so that $G/K$ is a global Hermitian symmetric space. Let…

We define analytic $R$-groups for affine Hecke algebras, and prove the analog of the Knapp-Stein Dimension Theorem. As a corollary we prove that the commutant algebra of a unitary principal series representation is isomorphic to the complex…

The endomorphism algebras of the permutation modules for transitive permutation groups, known as Hecke algebras, are fundamental objects in representation theory. While group algebras are known to be symmetric over any field, it is natural…

Let $G$ be a direct product of inner forms of general linear groups over non-archimedean locally compact fields of residue characteristic $p$ and let $K^1$ be the pro-$p$-radical of a maximal compact open subgroup of $G$. In this paper we…

This paper introduces the notion of calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The main results are that (1) irreducible calibrated…

Suppose $\ell$ is a prime number, $\ell >3$, $K$ is a field that is an unramified finite extension of the field $\Q_\ell$ of $\ell$-adic numbers, and $G$ is a finite group that is a semi-direct product of a normal $\ell'$-subgroup $H$ and a…

Let $F$ be a non-archimedean local field of odd residue characteristic $p$. Let $G$ be the unramified unitary group $U(2, 1)(E/F)$, and $K$ be a maximal compact open subgroup of $G$. For an $\overline{\mathbf{F}}_p$-smooth representation…

Let $(W,S)$ be a Coxeter system with $I\subseteq S$ such that the parabolic subgroup $W_I$ is finite. Associated to this data there is a \textit{Hecke algebra} $\scH$ and a \textit{parabolic Hecke algebra}…

Let $G$ be a split Kac-Moody group over a non-Archimedean local field, and let $\mathcal{H}$ be the Iwahori-Hecke algebra of $G$. In this paper, we construct a completed Iwahori-Hecke algebra $\widehat{\mathcal{H}}$ and prove that it…

The Lascoux-Leclerc-Thibon-Ariki theory asserts that the K-group of the representations of the affine Hecke algebras of type A is isomorphic to the algebra of functions on the maximal unipotent subgroup of the group associated with a Lie…

For a weighted graph $E$, we construct representation graphs $F$, and consequently, $L_K(E)$-modules $V_F$, where $L_K(E)$ is the Leavitt path algebra associated to $E$, with coefficients in a field $K$. We characterise representation…

In this article we introduce a framization of the Hecke algebra of type B. For this framization we construct a faithful tensorial representation and two linear bases. We finally construct a Markov trace on these algebras and from this trace…