Semisimple and cuspidal characters of gl<sub>n</sub>(0)

Hill, Gregory

doi:10.1080/00927879508825204

Cited by 20 publications

(26 citation statements)

References 5 publications

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“…In later publications [11][12][13], he succeeded in constructing many irreducible representations (namely strongly-semisimple, semisimple, regular, etc.) for these groups.…”

Section: Introductionmentioning

confidence: 98%

On representations of general linear groups over principal ideal local rings of length two

Singla

2010

Journal of Algebra

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We study the irreducible complex representations of general linear groups over principal ideal local rings of length two with a fixed finite residue field. We construct a canonical correspondence between the irreducible representations of all such groups that preserves dimensions. For general linear groups of order three and four over these rings, we construct all the irreducible representations. We show that the problem of constructing all the irreducible representations of all general linear groups over these rings is not easier than the problem of constructing all the irreducible representations of all general linear groups over principal ideal local rings of arbitrary length in the function field case.

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“…In later publications [11][12][13], he succeeded in constructing many irreducible representations (namely strongly-semisimple, semisimple, regular, etc.) for these groups.…”

Section: Introductionmentioning

confidence: 98%

On representations of general linear groups over principal ideal local rings of length two

Singla

2010

Journal of Algebra

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“…The latter are closely related to unramified maximal tori and the unramified discrete series representations of p-adic groups, and this is another reason for our choice of terminology. There is also some overlap with the representations constructed by Hill [8,9] in the case G = GL n , again by a non-cohomological method.…”

Section: Representations Of Reductive Groups Over Finite Rings 637mentioning

confidence: 99%

Unramified representations of reductive groups over finite rings

Stasinski

2009

Represent. Theory

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Abstract. Lusztig has given a construction of certain representations of reductive groups over finite local principal ideal rings of characteristic p, extending the construction of Deligne and Lusztig of representations of reductive groups over finite fields. We generalize Lusztig's results to reductive groups over arbitrary finite local rings. This generalization uses the Greenberg functor and the theory of group schemes over Artinian local rings.

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“…Nevertheless, only in a very recent preprint [31] by Stasinski all the irreducible representations of GL 2 (o ) are constructed for general o. For higher dimensions there are some partial results of a more general nature by Hill [8][9][10][11], Lusztig [18] and Aubert, Onn, Prasad and Stasinski [1] however, the general case still remains out of reach.…”

Section: History Of the Problemmentioning

confidence: 98%

Representations of automorphism groups of finiteo-modules of rank two

Onn

2008

Advances in Mathematics

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Let o be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite o-module M of rank two. The main emphasis is on the interaction between the different groups and their representations. An induction scheme is developed in order to study the whole family of these groups coherently. The results obtained depend on the ring o in a very weak manner, mainly through the degree of the residue field. In particular, a uniform description of the irreducible representations of GL 2 (o/p ) is obtained, where p is the maximal ideal of o.

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Semisimple and cuspidal characters of gl_n(0)

Cited by 20 publications

References 5 publications

On representations of general linear groups over principal ideal local rings of length two

On representations of general linear groups over principal ideal local rings of length two

Unramified representations of reductive groups over finite rings

Representations of automorphism groups of finiteo-modules of rank two

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Semisimple and cuspidal characters of gln(0)

Cited by 20 publications

References 5 publications

On representations of general linear groups over principal ideal local rings of length two

On representations of general linear groups over principal ideal local rings of length two

Unramified representations of reductive groups over finite rings

Representations of automorphism groups of finiteo-modules of rank two

Contact Info

Product

Resources

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Semisimple and cuspidal characters of gl_n(0)