Howlett, R. B.; Lehrer, G. I. On Harish-Chandra induction and restriction for modules of Levi subgroups. (English) Zbl 0802.20036 J. Algebra 165, No. 1, 172-183 (1994). Let \(G\) be a finite group with split \(BN\) pair, obtained as the group of \({\mathbf F}_ q\)-rational points in a connected reductive group. The authors study the dependence on the parabolic subgroup \(P\) of the Harish- Chandra induction functor \({\mathbf R}^ G_{L\subset P}\), where \(L\) is a Levi subgroup of \(P\). Over a base ring \(R\) in which the characteristic \(p\) of \({\mathbf F}_ q\) is invertible, they construct an explicit isomorphism \({\mathbf R}^ G_{L \subset P} \to {\mathbf R}^ G_{L \subset P'}\), when \(P'\) is another parabolic subgroup with \(L\) as Levi subgroup. They also show by example that the functors need not be isomorphic when \(p\) fails to be invertible in \(R\). Reviewer: W.van der Kallen (Utrecht) Cited in 18 Documents MSC: 20G05 Representation theory for linear algebraic groups 20G40 Linear algebraic groups over finite fields 20E42 Groups with a \(BN\)-pair; buildings Keywords:group of rational points; finite group with split \(BN\) pair; connected reductive group; parabolic subgroup; Harish-Chandra induction functor; Levi subgroup PDFBibTeX XMLCite \textit{R. B. Howlett} and \textit{G. I. Lehrer}, J. Algebra 165, No. 1, 172--183 (1994; Zbl 0802.20036) Full Text: DOI