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G(l, k, d)-modules via groupoids
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Univ Bonn, Math Inst, D-53115 Bonn, Germany..
2016 (English)In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 43, no 1, 11-32 p.Article in journal (Refereed) Published
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Abstract [en]

In this note, we describe a seemingly new approach to the complex representation theory of the wreath product , where G is a finite abelian group. The approach is motivated by an appropriate version of Schur-Weyl duality. We construct a combinatorially defined groupoid in which all endomorphism algebras are direct products of symmetric groups and prove that the groupoid algebra is isomorphic to the group algebra of . This directly implies a classification of simple modules. As an application, we get a Gelfand model for from the classical involutive Gelfand model for the symmetric group. We describe the Schur-Weyl duality which motivates our approach and relate it to various Schur-Weyl dualities in the literature. Finally, we discuss an extension of these methods to all complex reflection groups of type G(l, k, d).

Place, publisher, year, edition, pages
2016. Vol. 43, no 1, 11-32 p.
Keyword [en]
Schur-Weyl duality, Wreath product, Simple module, Groupoid
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-275534DOI: 10.1007/s10801-015-0623-0ISI: 000367611700002OAI: oai:DiVA.org:uu-275534DiVA: diva2:900654
Funder
Swedish Research CouncilKnut and Alice Wallenberg FoundationThe Royal Swedish Academy of Sciences
Available from: 2016-02-04 Created: 2016-02-04 Last updated: 2017-11-30Bibliographically approved

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Mazorchuk, Volodymyr

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