×

On Harish-Chandra induction and restriction for modules of Levi subgroups. (English) Zbl 0802.20036

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 \(R\).

MSC:

20G05 Representation theory for linear algebraic groups
20G40 Linear algebraic groups over finite fields
20E42 Groups with a \(BN\)-pair; buildings
PDFBibTeX XMLCite
Full Text: DOI