首页/论文/2003.02715

arXiv 2003.027152020-03-05math.RT

On induction of class functions

G. Lusztig

备注：: 11 pages

英文摘要：

Let G be a connected reductive group defined over a finite field F_q and let L be the Levi subgroup (defined over F_q) of a parabolic subgroup P of G. We define a linear map from class functions on L(F_q) to class functions on G(F_q). This map is independent of the choice of P. We show that for large q this map coincides with the known cohomological induction (whose definition involves a choice of P).

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Universal hierarchical structure of reducibility of Harish-Chandra parabolic induction

Given a supercuspidal representation $σ$ of a parabolic subgroup $P$ of reductive group $G$, we discover a universal hierarchical structure of reducibility of the parabolic induction $Ind^G_P(σ)$, i.e. always irreducible from some Levi-level up. As its applications, we provide a new simple proof of the generic irreducibility property of parabolic induction, and prove Clozel's finiteness conjecture of special exponents under some conditions. Indeed, those conditions are predicted by two conjectures of Shahidi which in some sense are proved for classical groups by Arthur in his monumental book--…

2019-10-12math.RT

The Exterior Cubic L-function of GU(6) and Unitary Automorphic Induction

In this paper, we extend Ginzburg-Rallis' integral representation for the exterior cube automorphic $L$-function of ${\rm GL}_6\times {\rm GL}_1$ to that of the quasi-split unitary similitude group ${\rm GU}_6$ and establish its analytic properties to determine the poles of this $L$-function. Furthermore, we introduce the automorphic induction for automorphic representations of ${\rm GU}_n$ and then show that the weak Langlands functorial lift for the automorphic induction exists for generic cuspidal automorphic representations. By using this automorphic induction, we give a conjectural criter…

2019-03-11math.NTmath.RT

Generalized induction of Kazhdan-Lusztig cells

Following Lusztig, we consider a Coxeter group $W$ together with a weight function. Geck showed that the Kazhdan-Lusztig cells of $W$ are compatible with parabolic subgroups. In this paper, we generalize this argument to some subsets of $W$ which may not be parabolic subgroups. We obtain two applications: we show that under specific technical conditions on the parameters, the cells of a certain finite parabolic subgroup of $W$ are cells in the whole group, and we decompose the affine Weyl group $\tilde{G}_{2}$ into left and two-sided cells for a whole class of weight functions.

2008-10-28math.RT

A new canonical induction formula for $p$-permutation modules

Applying Robert Boltje's theory of canonical induction, we give a restriction-preserving formula expressing any $p$-permutation module as a $\mathbb{Z}[1/p]$-linear combination of modules induced and inflated from projective modules associated with subquotient groups. The underlying constructions include, for any given finite group, a ring with a $\mathbb{Z}$-basis indexed by conjugacy classes of triples $(U, K, E)$ where $U$ is a subgroup, $K$ is a $p'$-residue-free normal subgroup of $U$ and $E$ is an indecomposable projective module of the group algebra of $U/K$.

2018-11-07math.RT

Generalized Artin and Brauer induction for compact Lie groups

Let G be a compact Lie group. We present two induction theorems for certain generalized G-equivariant cohomology theories. The theory applies to G-equivariant K-theory K_G, and to the Borel cohomology associated to any complex oriented cohomology theory. The coefficient ring of K_G is the representation ring R(G) of G. When G is a finite group the induction theorems for K_G coincide with the classical Artin and Brauer induction theorems for R(G).

2008-06-15math.ATmath.RT

A variant of the induction theorem for Springer representations

Let G be a simple algebraic group over C with the Weyl group W. For a unipotent element u of G, let B_u be the variety of Borel subgroups of G containing u. Let L be a Levi subgroup of a parabolic subgroup of G with the Weyl subgroup W_L. Assume that u is in L and let B_u^L be the corresponding variety for L. The induction theorem of Springer representations describes the W-module structure of H*(B_u) in terms of the W_L-module structure of H*(B_u^L). In this paper, we prove a certain refinement of the induction theorem by considering the action of a cyclic group of order e on H^*(B_u). As a c…

2006-07-04math.RT

更多相关论文收起更多论文

正深度 Deligne--Lusztig 诱导的 Green 函数

Green functions for positive-depth Deligne--Lusztig induction

本文在剩余域充分大条件下显式描述了非分歧椭圆对的正深度 Deligne--Lusztig 诱导，给出 Kaletha 正则 $L$-包的几何实现，并通过比较代数与几何两类 Green 函数证明正深度 Springer 假设。

2025-06-04math.NTmath.RT

Geometric approach to parabolic induction

In this note we construct a "restriction" map from the cocenter of a reductive group G over a local non-archimedean field F to the cocenter of a Levi subgroup. We show that the dual map corresponds to parabolic induction and deduce that parabolic induction preserves stability. We also give a new (purely geometric) proof that the character of normalized parabolic induction does not depend on a parabolic subgroup. In the appendix, we use a similar argument to extend a theorem of Lusztig-Spaltenstein on induced unipotent classes to all infinite fields.

2018-10-10math.AGmath.RT

Formulae for two-variable Green functions

Based on results of Digne-Michel-Lehrer (2003) we give two formulae for two-variable Green functions attached to Lusztig induction in a finite reductive group. We present applications to explicit computation of these Green functions, to conjectures of Malle and Rotilio, and to scalar products between Lusztig inductions of Gelfand-Graev characters.

2021-06-03math.GRmath.RT

On parabolic induction on inner forms of the general linear group over a non-archimedean local field

We give new criteria for the irreducibility of parabolic induction on the general linear group and its inner forms over a local non-archimedean field. In particular, we give a necessary and sufficient condition when the inducing data is of the form $π\otimesσ$ where $π$ is a ladder representation and $σ$ is an arbitrary irreducible representation. As an application we simplify the proof of the classification of the unitary dual.

2015-12-14math.NTmath.RT

pro-$p$ Iwahori-Hecke 模同伦范畴中的抛物诱导

Parabolic induction in the homotopy category of pro-$p$ Iwahori-Hecke modules

本文利用 Hovey 的 Gorenstein 投射模型结构研究 pro-$p$ Iwahori-Hecke 模的抛物诱导函子，证明相应同伦范畴与由抛物诱导本质像生成的厚子范畴构成 recollement，并对 $\mathrm{GL}_n$ 的单超奇异模给出完全分类。

2025-07-21math.CTmath.NTmath.RT