ISSN:
1572-9036
Keywords:
22C35
;
22E45
;
22E70
;
81C40
;
Polynomial representations
;
symplectic groups
;
Weyl's branching laws
;
invariant differentiation inner product
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The irreducible finite dimensional representations of the symplectic groups are realized as polynomials on the irreducible representation spaces of the corresponding general linear groups. It is shown that the number of times an irreducible representation of a maximal symplectic subgroup occurs in a given representation of a symplectic group, is related to the betweenness conditions of representations of the corresponding general linear groups. Using this relation, it is shown how to construct polynomial bases for the irreducible representation spaces of the symplectic groups in which the basis labels come from the representations of the symplectic subgroup chain, and the multiplicity labels come from representations of the odd dimensional general linear groups, as well as from ℂ subgroups. The irreducible representations of Sp(4) are worked out completely, and several examples from Sp(6) are given.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00047536
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