图塔的紧支持上同调和局部域上PGL n的一般表示

IF 0.8 4区数学 Q2 MATHEMATICS Comptes Rendus Mathematique Pub Date : 2023-10-24 DOI:10.5802/crmath.485

Anis Rajhi

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引用次数: 0

摘要

设F是一个非阿基米德局部紧化场，并设gn是群PGL n (F)。在本文中，我们在gn的Bruhat-Tits建筑的一个骨架上构建了一个塔(X ~ k) k小于0的图形。证明了G n的非球面不可约一般复表示可以作为图X ~ k的紧支持上同调的商来实现，且k足够大。此外，当表示是倒立的，那么它在这样的模型中有一个独特的实现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Compactly supported cohomology of a tower of graphs and generic representations of PGL n over a local field

Let F be a non-archimedean locally compact field and let G n be the group PGL n (F). In this paper we construct a tower (X ˜ k ) k⩾0 of graphs fibred over the one-skeleton of the Bruhat–Tits building of G n . We prove that a non-spherical and irreducible generic complex representation of G n can be realized as a quotient of the compactly supported cohomology of the graph X ˜ k for k large enough. Moreover, when the representation is cuspidal then it has a unique realization in a such model.

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来源期刊

Comptes Rendus Mathematique 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

115

审稿时长

16.6 weeks

期刊介绍： The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English. The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.