The cohomology of \(SL_ 2(F_ p)\) and the Hecke algebra actions
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 \(B\setminus GL(3,F)/B\).
scientific article; zbMATH DE number 3983480
scientific article