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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: It is well known that an invertible matrix admits a factorization as a product of a lower triangular matrix $L$ and an upper triangular matrix $U$ 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 $\overline B{}^-\overline B$ of a reductive monoid, where $B$ and $B^-$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

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