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

Journal Article · Wed Jan 15 00:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4861706· OSTI ID:22251137

Gould, Mark D.; Isaac, Phillip S.; Werry, Jason L. ^[1]

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1. School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072 (Australia)

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.

• OSTI ID: 22251137
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENVALUES
GRADED LIE GROUPS
IRREDUCIBLE REPRESENTATIONS
MATRIX ELEMENTS