Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)

Journal Article · Tue Dec 15 00:00:00 EST 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4938076· OSTI ID:22479560

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

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

The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible gl(m|n) modules. In particular, we give matrix element formulae for all gl(m|n) generators, including the non-elementary generators, together with their phases on finite dimensional type 2 unitary irreducible representations which include the contravariant tensor representations and an additional class of essentially typical representations. Remarkably, we find that the type 2 unitary matrix element equations coincide with the type 1 unitary matrix element equations for non-vanishing matrix elements up to a phase.

• OSTI ID: 22479560
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 12; Other Information: (c) 2015 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
DUALITY
EQUATIONS
GRADED LIE GROUPS
IRREDUCIBLE REPRESENTATIONS
MATRIX ELEMENTS
TENSORS