An analogue of the Steinberg character for the general linear group over the integers modulo a prime power

Peter S Campbell

doi:10.1016/j.jalgebra.2004.07.023

An analogue of the Steinberg character for the general linear group over the integers modulo a prime power

Peter S Campbell

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

Abstract

Lees, and independently Hill, described an irreducible character of GL(n) (Z/p(h)Z) for h > 1, which is an analogue of the Steinberg character in the h = 1 case. We give a new construction of this analogue. In particular, we prove that it is induced from the Steinberg character of an appropriate parabolic subgroup. Further, we use this to show that it has a characterisation identical to that given by Curtis to the Steinberg character. (C) 2004 Elsevier Inc. All rights reserved.

Translated title of the contribution	An analogue of the Steinberg character for the general linear group over the integers modulo a prime power
Original language	English
Pages (from-to)	368 - 385
Number of pages	18
Journal	Journal of Algebra
Volume	282 (1)
DOIs	https://doi.org/10.1016/j.jalgebra.2004.07.023
Publication status	Published - 1 Dec 2004

Bibliographical note

Publisher: Academic Press
Other identifier: IDS Number: 868RK

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10.1016/j.jalgebra.2004.07.023

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title = "An analogue of the Steinberg character for the general linear group over the integers modulo a prime power",

abstract = "Lees, and independently Hill, described an irreducible character of GL(n) (Z/p(h)Z) for h > 1, which is an analogue of the Steinberg character in the h = 1 case. We give a new construction of this analogue. In particular, we prove that it is induced from the Steinberg character of an appropriate parabolic subgroup. Further, we use this to show that it has a characterisation identical to that given by Curtis to the Steinberg character. (C) 2004 Elsevier Inc. All rights reserved.",

author = "Campbell, \{Peter S\}",

note = "Publisher: Academic Press Other identifier: IDS Number: 868RK ",

year = "2004",

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doi = "10.1016/j.jalgebra.2004.07.023",

language = "English",

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T1 - An analogue of the Steinberg character for the general linear group over the integers modulo a prime power

AU - Campbell, Peter S

N1 - Publisher: Academic Press Other identifier: IDS Number: 868RK

PY - 2004/12/1

Y1 - 2004/12/1

N2 - Lees, and independently Hill, described an irreducible character of GL(n) (Z/p(h)Z) for h > 1, which is an analogue of the Steinberg character in the h = 1 case. We give a new construction of this analogue. In particular, we prove that it is induced from the Steinberg character of an appropriate parabolic subgroup. Further, we use this to show that it has a characterisation identical to that given by Curtis to the Steinberg character. (C) 2004 Elsevier Inc. All rights reserved.

AB - Lees, and independently Hill, described an irreducible character of GL(n) (Z/p(h)Z) for h > 1, which is an analogue of the Steinberg character in the h = 1 case. We give a new construction of this analogue. In particular, we prove that it is induced from the Steinberg character of an appropriate parabolic subgroup. Further, we use this to show that it has a characterisation identical to that given by Curtis to the Steinberg character. (C) 2004 Elsevier Inc. All rights reserved.

U2 - 10.1016/j.jalgebra.2004.07.023

DO - 10.1016/j.jalgebra.2004.07.023

M3 - Article (Academic Journal)

SN - 1090-266X

VL - 282 (1)

SP - 368

EP - 385

JO - Journal of Algebra

JF - Journal of Algebra

ER -

An analogue of the Steinberg character for the general linear group over the integers modulo a prime power

Abstract

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