Representations of wreath products on cohomology of De Concini-Procesi compactifications
| dc.creator | Henderson, Anthony | |
| dc.date | 2003-07-30 | |
| dc.date.accessioned | 2026-07-07T04:59:57Z | |
| dc.date.available | 2026-07-07T04:59:57Z | |
| dc.description | The 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.description | 38 pages | |
| dc.identifier | https://arxiv.org/abs/math/0307383 | |
| dc.identifier | http://arxiv.org/abs/math/0307383 | |
| dc.identifier | Intern. Math. Res. Notices 2004:20 (2004), 983-1021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68202 | |
| dc.subject | Representation Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 20F55 (Primary) 14D99, 05A15 (Secondary) | |
| dc.title | Representations of wreath products on cohomology of De Concini-Procesi compactifications | |
| dc.type | text |