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F-regularity of large Schubert varieties
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 128, Number 4, August 2006
- pp. 949-962
- 10.1353/ajm.2006.0030
- Article
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Let G denote a connected reductive algebraic group over an algebraically closed field k and let X denote a projective G × G-equivariant embedding of G. The large Schubert varieties in X are the closures of the double cosets BgB, where B denotes a Borel subgroup of G, and g ε G. We prove that these varieties are globally F-regular in positive characteristic, resp. of globally F-regular type in characteristic 0. As a consequence, the large Schubert varieties are normal and Cohen-Macaulay.