In this paper a rather unconventional real basis for the real symplectic algebra sp(2n,R) is studied. This basis is valid for representations carried by homogeneous polynomials of the 2n phase‐space variables. The utility of this basis for practical computations is demonstrated by giving a simple derivation of the second‐ and fourth‐order indices of irreducible representations of sp(2n,R).
Topics
Representation theory
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The reader should be wamed that there are several conflicting notations in use for denoting the various symplectic algebras. The notation is often used to denote the real symplectic algebra Sometimes is used to denote this algebra. In this paper we have adopted the least ambiguous set of notations found in the literature. The real symplectic algebra is denoted by the complex symplectic algebra is denoted by the so-called unitary symplectic algebra is denoted by
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© 1992 American Institute of Physics.
1992
American Institute of Physics
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