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ON EXTERIOR POWERS OF REFLECTION REPRESENTATIONS

Part of: Basic linear algebra Representation theory of groups Special aspects of infinite or finite groups Metric geometry Algebraic combinatorics

Published online by Cambridge University Press:  06 October 2023

HONGSHENG HU Open the ORCID record for HONGSHENG HU [Opens in a new window]
HONGSHENG HU*
Affiliation:
Beijing International Center for Mathematical Research, Peking University, No. 5 Yiheyuan Road, Haidian District, Beijing 100871, PR China
*
e-mail: huhongsheng16@mails.ucas.ac.cn
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Abstract

In 1968, Steinberg [Endomorphisms of Linear Algebraic Groups, Memoirs of the American Mathematical Society, 80 (American Mathematical Society, Providence, RI, 1968)] proved a theorem stating that the exterior powers of an irreducible reflection representation of a Euclidean reflection group are again irreducible and pairwise nonisomorphic. We extend this result to a more general context where the inner product invariant under the group action may not necessarily exist.

Keywords

exterior powersgeneralised reflectionsreflection representations

MSC classification

Primary: 15A75: Exterior algebra, Grassmann algebras
Secondary: 05E10: Combinatorial aspects of representation theory 20C15: Ordinary representations and characters 20F55: Reflection and Coxeter groups 51F15: Reflection groups, reflection geometries

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 110 , Issue 1 , August 2024 , pp. 90 - 102
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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References

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