Skip Navigation

International Mathematics Research Notices (2004) 2004:983-1021 , doi:10.1155/S1073792804132510
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Henderson, A.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Copyright © 2004 Hindawi Publishing Corporation. All rights reserved.

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

Anthony Henderson

The wreath product W(r,n) of the cyclic group of order r and the symmetric group Sn 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.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?


This article has been cited by other articles:


Home page
 Int Math Res NoticesHome page
A. Henderson and E. Rains
The Cohomology of Real De Concini-Procesi Models of Coxeter Type
Int Math Res Notices, January 1, 2008; 2008(rnn001): rnn001 - 29.
[Abstract] [PDF]


Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.