User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse




Journal Article

Combinatorics of Finite Abelian Groups and Weil Representations


Dutta,  Kunal
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

There are no locators available
Fulltext (public)
There are no public fulltexts available
Supplementary Material (public)
There is no public supplementary material available

Dutta, K., & Prasad, A. (2015). Combinatorics of Finite Abelian Groups and Weil Representations. Pacific Journal of Mathematics, 275(2), 295-324. doi:10.2140/pjm.2015.275.295.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0024-48C9-3
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.