Commuting Pairs in the Centralizers of 2-Regular Matrices

InMn(k),kan algebraically closed field, we call a matrixl-regular if each eigenspace is at mostl-dimensional. We prove that the variety of commuting pairs in the centralizer of a 2-regular matrix is the direct product of various affine spaces and various determinantal varieties Zl,mobtained from mat...

Full description

Saved in:
Bibliographic Details
Published in:Journal of algebra 1999-04, Vol.214 (1), p.174-181
Main Authors: Neubauer, Michael G, Sethuraman, B.A
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:InMn(k),kan algebraically closed field, we call a matrixl-regular if each eigenspace is at mostl-dimensional. We prove that the variety of commuting pairs in the centralizer of a 2-regular matrix is the direct product of various affine spaces and various determinantal varieties Zl,mobtained from matrices over truncated polynomial rings. We prove that these varieties Zl,mare irreducible and apply this to the case of thek-algebra generated by three commuting matrices: we show that if one of the three matrices is 2-regular, then the algebra has dimension at mostn. We also show that such an algebra is always contained in a commutative subalgebra ofMn(k) of dimension exactlyn.
ISSN:0021-8693
1090-266X
DOI:10.1006/jabr.1998.7703