The Steinberg representation is irreducible

Abstract

We prove that the Steinberg representation of a connected reductive group over an infinite field is irreducible. For finite fields, this is a classical theorem of Steinberg and Curtis.

arXiv comment28 pages, major revision, to appear in Duke Math. J

References in corpus (8)

• Integrality in the Steinberg module and the top-dimensional cohomology of SL_n(O_K)
• The codimension-one cohomology of SL_n Z
• Some Infinite Dimensional Representations of Reductive Groups with Frobenius Maps
• Stability in the high-dimensional cohomology of congruence subgroups
• Non-integrality of some Steinberg modules
• On the top dimensional cohomology groups of congruence subgroups of ${\text{SL}}_n(\mathbb{Z})$
• The dualizing module and top-dimensional cohomology group of ${\text{GL}}_n(\mathcal{O})$
• On the generalized Bykovskii presentation of Steinberg modules

Cited by in corpus (1)

• The decomposition of permutation module for infinite Chevalley groups, II