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The characteristic identities and reduced matrix elements of the unitary and orthogonal groups

Published online by Cambridge University Press:  17 February 2009

M. D. Gould
M. D. Gould
Affiliation:
Department of Mathematical Physics, The University of Adelaide, Adelaide, South Australia 5001
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Abstract

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Polynomial identities satisfied by the generators of the Lie groups O(n) and U(n) are rederived. Using these identities the reduced matrix elements of the Lie groups U(n) and O(n) are evaluated as rational functions of the IR labels occurring in the canonical chains

This method does not require an explicit realization of the Lie algebras and their representations using bosons. Finally, trace formulae encountered previously by several authors for finite dimensional irreducible representations are shown to hold on arbitrary representations admitting an infinitesimal character.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 4 , December 1978 , pp. 401 - 433
Copyright
Copyright © Australian Mathematical Society 1978

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