PreprintCC BY 4.0arXiv
A tensor square theorem for characters of GLn(q)
Abstract
We construct an irreducible character of GLn(q) whose square contains every irreducible character that is trivial on the centre of GLn(q). This character is related to, but in general not equal to, the Steinberg character. A key ingredient, which we also prove, is that every nonlinear irreducible character of GLn(q) that is trivial on the centre contains the trivial character when restricted to the diagonal subgroup T.
Related
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BibTeX
@misc{monteiro2026tensor,
title = {{A tensor square theorem for characters of $\operatornameGL_n(q)$}},
author = {Nariel Monteiro and Alexander Stasinski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17319},
eprint = {2609.17319},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17319},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A tensor square theorem for characters of GL_n(q)
AU - Nariel Monteiro
AU - Alexander Stasinski
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17319
UR - https://arxiv.org/abs/2609.17319
AB - We construct an irreducible character of GL_n(q) whose square contains every irreducible character that is trivial on the centre of GL_n(q). This character is related to, but in general not equal to, the Steinberg character. A key ingredient, which we also prove, is that every nonlinear irreducible character of GL_n(q) that is trivial on the centre contains the trivial character when restricted to the diagonal subgroup T.
ER -