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The Cohomology of the Regular Semisimple Variety

✍ Scribed by G.I Lehrer

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
265 KB
Volume
199
Category
Article
ISSN
0021-8693

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✦ Synopsis

We use the equivariant cohomology of hyperplane complements and their toral counterparts to give formulae for the Poincare polynomials of the varieties of Ε•egular semisimple elements of a reductive complex Lie group or Lie algebra. As a result, we obtain vanishing theorems for certain of the Betti numbers. Similar methods, using l-adic cohomology, may be used to compute numbers of rational points of the varieties over the finite field ‫ކ‬ . In the classical cases, one obtains, q both for the Poincare polynomials and for the numbers of rational points, polyno-αΈΏials which exhibit certain regularity conditions as the dimension increases. This regularity may be interpreted in terms of functional equations satisfied by certain power series, or in terms of the representation theory of the Weyl group.

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