B-Orbits in solutions to the equation X-2=0 in triangular matrices

Authors
Melnikov, A
Citation
A. Melnikov, B-Orbits in solutions to the equation X-2=0 in triangular matrices, J ALGEBRA, 223(1), 2000, pp. 101-108
Citations number
4
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF ALGEBRA
ISSN journal
00218693 → ACNP
Volume
223
Issue
1
Year of publication
2000
Pages
101 - 108
Database
ISI
SICI code
0021-8693(20000101)223:1<101:BISTTE>2.0.ZU;2-2
Abstract
Consider I-n(K), the set of solutions to the equation X-2 = 0 in n x n stri ctly upper-triangular matrices over field K. In this paper we construct the bijection from the set of adjoint orbits in I-n(K) onto the set of involut ions in symmetric group S-n. For a finite field K we compute the number of points in the orbits. (C) 2000 Academic Press.