Representations of wreath products on cohomology of De Concini-Procesi compactifications

dc.creatorHenderson, Anthony
dc.date2003-07-30
dc.date.accessioned2026-07-07T04:59:57Z
dc.date.available2026-07-07T04:59:57Z
dc.descriptionThe wreath product W(r,n) of the cyclic group of order r and the symmetric group S_n acts on the corresponding projective hyperplane complement, and on its wonderful compactification as defined by De Concini and Procesi. We give a formula for the characters of the representations of W(r,n) on the cohomology groups of this compactification, extending the result of Ginzburg and Kapranov in the r=1 case. As a corollary, we get a formula for the Betti numbers which generalizes the result of Yuzvinsky in the r=2 case. Our method involves applying to the nested-set stratification a generalization of Joyal's theory of tensor species, which includes a link between polynomial functors and plethysm for general r. We also give a new proof of Lehrer's formula for the representations of W(r,n) on the cohomology groups of the hyperplane complement.
dc.description38 pages
dc.identifierhttps://arxiv.org/abs/math/0307383
dc.identifierhttp://arxiv.org/abs/math/0307383
dc.identifierIntern. Math. Res. Notices 2004:20 (2004), 983-1021
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68202
dc.subjectRepresentation Theory
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subject20F55 (Primary) 14D99, 05A15 (Secondary)
dc.titleRepresentations of wreath products on cohomology of De Concini-Procesi compactifications
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