A combinatorial proof of Klyachko's Theorem on Lie representations
| dc.contributor.author | Kovacs, L | |
| dc.contributor.author | Stohr, Ralph | |
| dc.date.accessioned | 2015-12-07T22:48:05Z | |
| dc.date.issued | 2006 | |
| dc.date.updated | 2015-12-07T11:57:14Z | |
| dc.description.abstract | Let L be a free Lie algebra of finite rank r over an arbitrary field K of characteristic 0, and let L n denote the homogeneous component of degree n in L. Viewed as a module for the general linear group GL(r,K), L n is known to be semisimple with the isomorphism types of the simple summands indexed by partitions of n with at most r parts. Klyachko proved in 1974 that, for n > 6, almost all such partitions are needed here, the exceptions being the partition with just one part, and the partition in which all parts are equal to 1. This paper presents a combinatorial proof based on the Littlewood-Richardson rule. This proof also yields that if the composition multiplicity of a simple summand in L n is greater than 1, then it is at least n6-1. | |
| dc.identifier.issn | 0925-9899 | |
| dc.identifier.uri | http://hdl.handle.net/1885/26340 | |
| dc.publisher | Springer | |
| dc.source | Journal of Algebraic Combinatorics | |
| dc.subject | Keywords: Algebra; Computational complexity; Mathematical models; Numerical methods; Problem solving; Theorem proving; Composition multiplicity; Free Lie algebra; General linear group; Littlewood-Richardson rule; Combinatorial switching Free Lie algebra; General linear group; Littlewood-Richardson rule | |
| dc.title | A combinatorial proof of Klyachko's Theorem on Lie representations | |
| dc.type | Journal article | |
| local.bibliographicCitation.lastpage | 230 | |
| local.bibliographicCitation.startpage | 225 | |
| local.contributor.affiliation | Kovacs, L, College of Physical and Mathematical Sciences, ANU | |
| local.contributor.affiliation | Stohr, Ralph, College of Physical and Mathematical Sciences, ANU | |
| local.contributor.authoremail | repository.admin@anu.edu.au | |
| local.contributor.authoruid | Kovacs, L, u6300406 | |
| local.contributor.authoruid | Stohr, Ralph, t637 | |
| local.description.embargo | 2037-12-31 | |
| local.description.notes | Imported from ARIES | |
| local.identifier.absfor | 010105 - Group Theory and Generalisations | |
| local.identifier.ariespublication | u3488905xPUB44 | |
| local.identifier.citationvolume | 23 | |
| local.identifier.doi | 10.1007/s10801-006-7394-6 | |
| local.identifier.scopusID | 2-s2.0-33744738224 | |
| local.identifier.uidSubmittedBy | u3488905 | |
| local.type.status | Published Version |
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