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THE DECOMPOSITION OF PERMUTATION MODULE FOR INFINITE CHEVALLEY GROUPS, II

Part of: Representation theory of groups Special aspects of infinite or finite groups Linear algebraic groups and related topics

Published online by Cambridge University Press:  27 December 2024

JUNBIN DONG Open the ORCID record for JUNBIN DONG [Opens in a new window]
JUNBIN DONG*
Affiliation:
Institute of Mathematical Sciences ShanghaiTech University Shanghai 201210 China [email protected]
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Abstract

Let $\mathbf {G}$ be a connected reductive algebraic group over an algebraically closed field $\Bbbk $ and ${\mathbf B}$ be a Borel subgroup of ${\mathbf G}$. In this paper, we completely determine the composition factors of the permutation module $\mathbb {F}[{\mathbf G}/{\mathbf B}]$ for any field $\mathbb {F}$.

Keywords

Chevalley grouppermutation moduleflag variety

MSC classification

Primary: 20C07: Group rings of infinite groups and their modules 20G05: Representation theory
Secondary: 20F18: Nilpotent groups
Type
Article
Information
Nagoya Mathematical Journal , Volume 257 , March 2025 , pp. 156 - 169
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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References

Carter, R. W., Finite Groups of Lie Type: Conjugacy Classes and Complex Characters, Pure Appl. Math., John Wiley and Sons, New York, 1985.Google Scholar
Chen, X. and Dong, J., The permutation module on flag varieties in cross characteristic , Math. Z. 293 (2019), 475–484.CrossRefGoogle Scholar
Chen, X. and Dong, J., The decomposition of permutation module for infinite Chevalley groups , Sci. China Math 64 (2021), no. 5, 921–930.CrossRefGoogle Scholar
Geck, M., Kazhdan–Lusztig cells and the Murphy basis , Proc. Lond. Math. Soc. 93 (2006), no. 3, 635–665.CrossRefGoogle Scholar
Kazhdan, D. and Lusztig, G., Representations of Coxeter groups and Hecke algebras , Invent. Math. 53 (1979), 165–184.CrossRefGoogle Scholar
Putman, A. and Snowden, A., The Steinberg representation is irreducible , Duke Math. J. 172 (2023), 775–808.CrossRefGoogle Scholar
Serre, J. P., Linear Representations of Finite Groups, GTM, 42, Springer-Verlag, New York–Heidelberg, 1977.CrossRefGoogle Scholar
Xi, N., Some infinite dimensional representations of reductive groups with Frobenius maps , Sci. China Math. 57 (2014), 1109–1120.CrossRefGoogle Scholar
Yang, R., Irreducibility of infinite dimensional Steinberg modules of reductive groups with Frobenius maps , J. Algebra 533 (2019), 17–24.CrossRefGoogle Scholar