Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

Representations of monoids arising from finite groups of Lie type

Author(s): A. Salwa
Journal: Trans. Amer. Math. Soc. 348 (1996), 2931-2945.
MSC (1991): Primary 20M30, 20M25
MathSciNet review: 1351495
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: A class of finite monoids $M$ constructed from a group $G$ of Lie type is considered. We describe the irreducible complex representations and prove the complete reducibility of the representations of $M$. The sandwich matrix of $M$ is decomposed into a product of matrices corresponding to maximal parabolic subgroups of $G$.


References:

1.
Carter,R.W., Finite Groups of Lie Type : Conjugacy Classes and Complex Characters, Wiley, 1985.MR 87d:20060

2.
Clifford,A.H. and Preston,G.B., The Algebraic Theory of Semigroups, Math. Surveys, no.7, Amer. Math. Soc., Providence, R.I., 1961.MR 24:A2627

3.
Curtis,C.W. and Reiner,I., Methods of Representation Theory, Volumes 1,2, Wiley, New York, 1987.MR 88f:20002

4.
Howlett,R.B. and Lehrer,G.L., Induced cuspidal representations and generalised Hecke rings, Invent. Math. 58 (1980), 37-64.MR 81j:20017

5.
Kovacs,L.G., Semigroup algebras of the full matrix semigroups over a finite field, Proc. Amer. Math. Soc. 116 (1992), 911-917.MR 93b:16051

6.
Okninski,J. and Putcha,M.S., Complex representations of matrix semigroups, Trans. Amer. Math. Soc. 323 (1991), 563-581.MR 91e:20047

7.
Putcha,M.S., Monoids on groups with BN-pair, J. Algebra 120 (1989), 139-169.MR 89k:20091

8.
Putcha,M.S., Classification of monoids of Lie type, J. Algebra 163 (1994), 636-662.MR 95b:20089

9.
Putcha,M.S., Sandwich matrices, Solomon algebras and Kazhdan-Lusztig polynomials, Trans. Amer. Math. Soc. 340 (1993), 415-428.MR 94a:20112

10.
Putcha,M.S., Monoid Hecke algebras, preprint.

11.
Putcha,M.S., Big cell algebras I. Steinberg representation, preprint.

12.
Solomon,L., The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field, Geom. Dedicata 36 (1990), 15-39.MR 92e:20035


Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 20M30, 20M25

Retrieve articles in all Journals with MSC (1991): 20M30, 20M25


Additional Information:

A. Salwa
Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2,02-097 Warsaw, Poland
Email: asalwa@mimuw.edu.pl

DOI: 10.1090/S0002-9947-96-01621-2
PII: S 0002-9947(96)01621-2
Received by editor(s): February 3, 1995
Received by editor(s) in revised form: September 18, 1995
Additional Notes: Supported by KBN research grant 2 P301 051 06.
Copyright of article: Copyright 1996, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia