Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)

Gould, Mark D., Isaac, Phillip S. and Werry, Jason L. (2014) Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n). Journal of Mathematical Physics, 55 011703: 011703.1-011703.32. doi:10.1063/1.4861706

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Author Gould, Mark D.
Isaac, Phillip S.
Werry, Jason L.
Title Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)
Formatted title
Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)
Journal name Journal of Mathematical Physics   Check publisher's open access policy
ISSN 0022-2488
1089-7658
1527-2427
Publication date 2014-01-17
Sub-type Article (original research)
DOI 10.1063/1.4861706
Open Access Status File (Publisher version)
Volume 55
Issue 011703
Start page 011703.1
End page 011703.32
Total pages 32
Place of publication College Park, MD, United States
Publisher American Institute of Physics
Language eng
Formatted abstract
Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary generators, on finite dimensional type 1 unitary irreducible representations. We compare our results with existing works that deal with only subsets of the class of type 1 unitary representations, all of which only present explicit matrix elements for elementary generators. Our work therefore provides an important extension to existing methods, and thus highlights the strength of our techniques which exploit the characteristic identities.
Keyword Lie superalgebras
Unitary representations
Matrix element evaluation
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2015 Collection
 
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Created: Tue, 04 Mar 2014, 19:03:31 EST by Mark Gould on behalf of Mathematics