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Book Chapter
A LiE Subroutine for Computing Prehomogeneous Spaces Associated with Real Nilpotent Orbits
Book Series
Lecture Notes in Computer Science
Publisher
Springer Berlin / Heidelberg
ISSN
0302-9743 (Print) 1611-3349 (Online)
Volume
Volume 3482/2005
Book
Computational Science and Its Applications – ICCSA 2005
DOI
10.1007/b136271
Copyright
2005
ISBN
978-3-540-25862-9
Category
Symbolic Computation, SC 2005 Workshop
DOI
10.1007/11424857_54
Pages
512-521
Subject Collection
Computer Science
SpringerLink Date
Monday, May 02, 2005
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Symbolic Computation, SC 2005 Workshop
A LiE Subroutine for Computing Prehomogeneous Spaces Associated with Real Nilpotent Orbits
Steven Glenn Jackson
1
and Alfred G. Noël
1
(1)
Department of Mathematics, University of Massachusetts, Boston, MA 02125-3393, USA
Abstract
We describe an algorithm for decomposing certain modules attached to real nilpotent orbits into their irreducible components. These modules are prehomogeneous spaces in the sense of Sato and Kimura and arise in the study of nilpotent orbits and the representation theory of Lie groups. The output is a set of
statements that can be compiled in a
environment in order to produce tables. Although the algorithm is used to solve the problem in the case of exceptional real reductive Lie groups of inner type it does describe these spaces for the classical cases of inner type also. Complete tables for the exceptional groups can be found at http://www.math.umb.edu/~anoel/publications/tables/.
Steven
Glenn
Jackson
Email:
jackson@math.umb.edu
Alfred
G.
Noël
Email:
anoel@math.umb.edu
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