Abstract

The purpose of this paper is to present a new combinatorial criterion for rational smoothness of a point in a Schubert variety. The main result proves the criterion for Schubert varieties associated to partial flag varieties of the form G/P where G is semisimple of classical type and P is a maximal parabolic subgroup; in the case where G/P is of cominuscule type (not necessarily classical), we prove a stronger result. We conjecture that the criterion is valid for all Schubert varieties. The paper also contains some general results related to rational smoothness in Schubert varieties.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 317-356
Launched on MUSE
2003-03-26
Open Access
No
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