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On tensor operators and characteristic identities for semi-simple Lie algebras

Published online by Cambridge University Press:  17 February 2009

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

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Tensor identities for finite dimensional representations of arbitrary semi-simple Lie algebras are derived and are applied to the construction of left-projection operators which project out the shift components of tensor operators from the left. The corresponding adjoint identities are also derived and are used for the construction of right-projection operators. It is also shown that, on a finite dimensional irreducible representation, these identities may be considerably reduced. Commutation relations between the shift tensors of a tensor operator are also computed in terms of the roots appearing in the tensor identities.

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 3 , June 1978 , pp. 290 - 314
Copyright
Copyright © Australian Mathematical Society 1978

References

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