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  Combinatorics of Finite Abelian Groups and Weil Representations

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.

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Genre: Zeitschriftenartikel
Latex : Combinatorics of Finite Abelian Groups and {W}eil Representations

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 Urheber:
Dutta, Kunal1, Autor           
Prasad, Amritanshu2, Autor
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              
2External Organizations, ou_persistent22              

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Schlagwörter: Mathematics, Representation Theory, math.RT,Mathematics, Combinatorics, math.CO,Mathematics, Number Theory, math.NT,
 Zusammenfassung: 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.

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Sprache(n): eng - English
 Datum: 2010-10-182014-07-09201420152015
 Publikationsstatus: Erschienen
 Seiten: 26 pages, 3 figures Revised version, to appear in Pacific Journal of Mathematics
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: -
 Identifikatoren: BibTex Citekey: Dutta:1301026a
DOI: 10.2140/pjm.2015.275.295
 Art des Abschluß: -

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Titel: Pacific Journal of Mathematics
Genre der Quelle: Zeitschrift
 Urheber:
Affiliations:
Ort, Verlag, Ausgabe: Berkeley, CA : Mathematical Sciences Publisher
Seiten: - Band / Heft: 275 (2) Artikelnummer: - Start- / Endseite: 295 - 324 Identifikator: ISSN: 0030-8730
CoNE: https://pure.mpg.de/cone/journals/resource/954925431349