Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493270 | Journal of Algebra | 2005 | 16 Pages |
Abstract
Let G be a simple algebraic group over the algebraically closed field k. A slightly strengthened version of a theorem of T.A. Springer says that (under some mild restrictions on G and k) there exists a G-equivariant isomorphism of varieties Ï:UâN, where U denotes the unipotent variety of G and N denotes the nilpotent variety of g=LieG. Such Ï is called a Springer isomorphism. Let B be a Borel subgroup of G, U the unipotent radical of B and u the Lie algebra of U. In this note we show that a Springer isomorphism Ï induces a B-equivariant isomorphism ÏË:U/Mâu/m, where M is any unipotent normal subgroup of B and m=LieM. We call such a map ÏË a relative Springer isomorphism. We also use relative Springer isomorphisms to describe the geometry of U-orbits in u.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Simon M. Goodwin,