Big cells and LU factorization in reductive monoids

Author:
Mohan S. Putcha

Journal:
Proc. Amer. Math. Soc. **130** (2002), 3507-3513

MSC (2000):
Primary 20G99, 15A23

DOI:
https://doi.org/10.1090/S0002-9939-02-06515-2

Published electronically:
May 29, 2002

MathSciNet review:
1918826

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Abstract | References | Similar Articles | Additional Information

Abstract: It is well known that an invertible matrix admits a factorization as a product of a lower triangular matrix and an upper triangular matrix if and only if all the principal minors of the matrix are non-zero. The corresponding problem for singular matrices is much more subtle. We study this problem in the general setting of a reductive monoid and obtain a solution in terms of the Bruhat-Chevalley order. In the process we obtain a decomposition of the big cell of a reductive monoid, where and are opposite Borel subgroups of the unit group.

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Additional Information

**Mohan S. Putcha**

Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205

Email:
putcha@math.ncsu.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06515-2

Received by editor(s):
March 19, 2001

Received by editor(s) in revised form:
July 30, 2001

Published electronically:
May 29, 2002

Communicated by:
Stephen D. Smith

Article copyright:
© Copyright 2002
American Mathematical Society