Gelfand–Graev representation
In representation theory, a branch of mathematics, the Gelfand–Graev representation is a representation of a reductive group over a finite field introduced by {{harvtxt|Gelfand|Graev|1962}}, induced from a non-degenerate character of a Sylow subgroup.
The Gelfand–Graev representation is reducible and decomposes as the sum of irreducible representations, each of multiplicity at most 1. The irreducible representations occurring in the Gelfand–Graev representation are called regular representations. These are the analogues for finite groups of representations with a Whittaker model.
References
- {{Citation | last1=Carter | first1=Roger W. | author1-link=Roger Carter (mathematician) | title=Finite groups of Lie type. Conjugacy classes and complex characters. | url=https://books.google.com/books?id=LvvuAAAAMAAJ | publisher=John Wiley & Sons | location=New York | series=Pure and Applied Mathematics (New York) | isbn=978-0-471-90554-7 | mr=794307 | year=1985}}
- {{Citation | last1=Gelfand | first1=I. M. | authorlink=Israel Gelfand | last2=Graev | first2=M. I. | authorlink2=Mark Iosifovich Graev| title=Construction of irreducible representations of simple algebraic groups over a finite field | mr=0148765 | year=1962 | journal=Doklady Akademii Nauk SSSR | issn=0002-3264 | volume=147 | pages=529–532}} English translation in volume 2 of Gelfand's collected works.
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