相关论文: Bernstein-Zelevinsky derivatives, branching rules …

Let F be a nonarchimedean local field of odd residual characteristic p. We classify finite-dimensional simple right modules for the pro-p-Iwahori-Hecke algebra $\mathcal{H}_C(G,I(1))$, where G is the unramified unitary group U(2,1)(E/F) in…

For a finite central extension $\tilde{G}$ of a classical $p$-adic reductive group, we consider the endomorphism algebra of some induced projective generator \`a la Bernstein of the category of smooth representations of $\tilde{G}$. In the…

Let $g$ be a complex semisimple Lie algebra with Weyl group $W$. Let $H(W)$ be the Iwahori-Hecke algebra associated to $W$. For each $w\in W$, let $T_w$ and $C_w$ be the corresponding $Z$-graded twisting functor and $Z$-graded shuffling…

Let $H$ be a complex reductive group, with finite-dimensional representations $W$ and $U$. The module of covariants for $W$ of type $U$ is the space of all $H$-equivariant polynomial maps $\varphi: W \longrightarrow U$. In this paper, we…

The graded Iwahori--Matsumoto involution $\mathbb{IM}$ is an algebra involution on a graded Hecke algebra closely related to the more well-known Iwahori--Matsumoto involution on an affine Hecke algebra. It induces an involution on the…

For the p-adic group G=SL (2) , we present results of the computations of the sums of the Bernstein projectors of a given depth. Motivation for the computations is based on a conversation with Roger Howe in August 2013. The computations are…

This paper provides a unified approach to results on representations of affine Hecke algebras, cyclotomic Hecke algebras, affine BMW algebras, cyclotomic BMW algebras, Markov traces, Jacobi-Trudi type identities, dual pairs (Zelevinsky),…

This article gives conceptual statements and proofs relating parabolic induction and Jacquet functors on split reductive groups over a non-Archimedean local field to the associated Iwahori-Hecke algebra as tensoring from and restricting to…

This is an extended and corrected version of the author's Diplomarbeit. A class of algebras called generic pro-$p$ Hecke algebras is introduced, enlarging the class of generic Hecke algebras by considering certain extensions of (extended)…

We study a BGG-type category of infinite dimensional representations of H[W], a semi-direct product of the quantum torus with parameter `q' built on the root lattice of a semisimple group G, and the Weyl group of G. Irreducible objects of…

The main result describes the Brauer-Nesbitt reduction of unipotent representations of a finite group of Lie type, expressing it as an explicit linear combination of the restriction of Weyl modules from the algebraic group to the group of…

Let $p$ be an odd prime. Let $F$ be a non-archimedean local field of residue characteristic $p$, and let $\mathbb{F}_q$ be its residue field. Let $\mathcal{H}^{(1)}_{\mathbb{F}_q}$ be the pro-$p$-Iwahori-Hecke algebra of the $p$-adic group…

We study Kostant cohomology and Bernstein-Gelfand-Gelfand resolutions for finite dimensional representations of basic classical Lie superalgebras and reductive Lie superalgebras based on them. For each choice of parabolic subalgebra and…

We propose a geometric framework to produce a formula relating higher period integrals to higher central derivatives of $L$-functions over function fields, extending the framework of relative Langlands duality \`a la…

Let $G$ be the group of rational points of a split connected reductive group over a nonarchimedean local field of residue characteristic $p$. Let $I$ be a pro-$p$ Iwahori subgroup of $G$ and let $R$ be a commutative quasi-Frobenius ring. If…

For a split reductive group ${}^L G$ over a global field, we determine the spectrum of the spherical Hecke algebra coming from the unramified Eisenstein series for the minimal parabolic ${}^L B$. This is done using a certain decomposition…

Let H(G) be the Hecke algebra of a reductive p-adic group G. We formulate a conjecture for the ideals in the Bernstein decomposition of H(G). The conjecture says that each ideal is geometrically equivalent to an algebraic variety. Our…

We construct an exact functor from the category of Harish-Chandra modules of $\mathrm{GL}_n(\mathbb C)$ to the category of finite-dimensional modules of graded Hecke algebras of type A. We show that the functor preserves parabolically…

We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ${\mathbb Q}$, acting on…

The Bernstein degree ($\operatorname{Deg}$) is a fundamental invariant of admissible representations of a real reductive Lie group $G_{\mathbb{R}}$. Our main result concerns the classical dual pairs $(G_{\mathbb{R}}, H_{\mathbb{R}}(k))$,…