Generalized Steinberg representations of split reductive linear algebraic groups

Details Generalized Steinberg representations of split reductive linear algebraic groups Generalized Steinberg representations of split reductive linear algebraic groups

2009-11-03

arxiv.org/abs/0911.0578v1

C. R. Acad. Sci. Paris, Ser. I 348 (2010), p. 243-248

Mathematics

Representation Theory

17 pages

Scientific paper

We generalize results of P. Schneider and U. Stuhler for GL_l+1 to a reductive algebraic group G defined and split over a non-archimedean local field K. Following their lines, we prove that the generalized Steinberg representations of G with coefficients in any abelian group are cyclic. When G is semi-simple of adjoint type, we give an expression of these representations, whenever it is possible and in particular for those that are of maximal degree, in terms of the parahoric subgroups of G.

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