The Steinberg representation is irreducible
Andrew Putman, Andrew Snowden
TL;DR
This paper proves that the Steinberg representation of a connected reductive group over an infinite field is irreducible, extending classical results known for finite fields.
Contribution
It establishes the irreducibility of the Steinberg representation over infinite fields, generalizing previous finite field results.
Findings
Steinberg representation is irreducible over infinite fields
Generalization of classical finite field results
Supports broader understanding of reductive group representations
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.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Molecular spectroscopy and chirality