The cohomology of \(SL_ 2(F_ p)\) and the Hecke algebra actions
type: Item
instance of: scholarly article
title: The cohomology of \(SL_ 2(F_ p)\) and the Hecke algebra actions
zbMATH Open document ID: 0608.20029
author: Michishige Tazuka
published in: Kodai Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: Let p be a prime number, F the field with p elements, S the symmetric algebra on \(F^ 2\). The author computes \(H^*(SL(2,F),S)\) along with the action on it of GL(2,F). Next is computed \(H^*(GL(2,F),A)\) where A is S or a one-dimensional GL(2,F)-module. Finally, let B denote a Borel subgroup of GL(3,F). The author determines the p-part of \(H^*(B,{\mathbb{Z}})\) modulo nilpotents along with the action on it of the double cosets \(B\setminus GL(3,F)/B\).
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 3983480
zbMATH Keywords: cohomology group
zbMATH Keywords: Hecke algebra actions
zbMATH Keywords: symmetric algebra
zbMATH Keywords: Borel subgroup
zbMATH Keywords: double cosets
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138037273
OpenAlex ID: W1980514914
cites work: The cohomology of the \(GL_2\) of a finite field
cites work: Q5670826
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cites work: Cohomology of finite groups of Lie type. I
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cites work: Hecke operators in cohomology of groups
cites work: The mod p cohomology ring of \(GL_ 3(F_ p)\)
cites work: Q5510956
DOI: 10.2996/KMJ/1138037273
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description: scientific article; zbMATH DE number 3983480