A generalization of Steinberg's cross section
Let G be a semisimple group over an algebraically closed field. Steinberg has associated to a Coxeter element w of minimal length r a subvariety V of G isomorphic to an affine space of dimension r which meets the regular unipotent class Y in exactly one point. In this paper this is generalized to th...
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| Format: | Article |
| Language: | English |
| Published: |
American Mathematical Society,
2012-06-14T20:19:25Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | Let G be a semisimple group over an algebraically closed field. Steinberg has associated to a Coxeter element w of minimal length r a subvariety V of G isomorphic to an affine space of dimension r which meets the regular unipotent class Y in exactly one point. In this paper this is generalized to the case where w is replaced by any elliptic element in the Weyl group of minimal length d in its conjugacy class, V is replaced by a subvariety V' of G isomorphic to an affine space of dimension d, and Y is replaced by a unipotent class Y' of codimension d in such a way that the intersection of V' and Y' is finite. National Science Foundation (U.S.) (grant DMS-0758262) Research Grants Council of Hong Kong, China (grant 601409) |
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