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Free keywords:
Mathematics, Representation Theory, math.RT,Mathematics, Combinatorics, math.CO,Mathematics, Number Theory, math.NT,
Abstract:
The Weil representation of the symplectic group associated to a finite
abelian group of odd order is shown to have a multiplicity-free decomposition.
When the abelian group is p-primary, the irreducible representations occurring
in the Weil representation are parametrized by a partially ordered set which is
independent of p. As p varies, the dimension of the irreducible representation
corresponding to each parameter is shown to be a polynomial in p which is
calculated explicitly. The commuting algebra of the Weil representation has a
basis indexed by another partially ordered set which is independent of p. The
expansions of the projection operators onto the irreducible invariant subspaces
in terms of this basis are calculated. The coefficients are again polynomials
in p. These results remain valid in the more general setting of finitely
generated torsion modules over a Dedekind domain.
