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

## 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.

- Authors:

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

- Publication Date:

- OSTI Identifier:
- 22251657

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENVALUES; GRADED LIE GROUPS; IRREDUCIBLE REPRESENTATIONS; MATRIX ELEMENTS

### Citation Formats

```
Gould, Mark D., Isaac, Phillip S., and Werry, Jason L..
```*Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)*. United States: N. p., 2014.
Web. doi:10.1063/1.4861706.

```
Gould, Mark D., Isaac, Phillip S., & Werry, Jason L..
```*Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)*. United States. doi:10.1063/1.4861706.

```
Gould, Mark D., Isaac, Phillip S., and Werry, Jason L.. Wed .
"Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)". United States.
doi:10.1063/1.4861706.
```

```
@article{osti_22251657,
```

title = {Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)},

author = {Gould, Mark D. and Isaac, Phillip S. and Werry, Jason L.},

abstractNote = {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.},

doi = {10.1063/1.4861706},

journal = {Journal of Mathematical Physics},

number = 1,

volume = 55,

place = {United States},

year = {Wed Jan 15 00:00:00 EST 2014},

month = {Wed Jan 15 00:00:00 EST 2014}

}

DOI: 10.1063/1.4861706

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