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Split subvarieties of group embeddings


Author: Nicolas Perrin
Journal: Trans. Amer. Math. Soc. 367 (2015), 8421-8438
MSC (2010): Primary 14M27; Secondary 20G15, 13A35
DOI: https://doi.org/10.1090/S0002-9947-2015-06279-5
Published electronically: March 20, 2015
MathSciNet review: 3403060
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Abstract: Let $ G$ be a connected reductive group and $ X$ an equivariant compactification of $ G$. In $ X$, we study generalised and opposite generalised Schubert varieties, and their intersections called generalised Richardson varieties and projected generalised Richardson varieties. Any complete $ G$-embedding has a canonical Frobenius splitting, and we prove that the compatibly split subvarieties are the generalised projected Richardson varieties extending a result of Knutson, Lam and Speyer to the situation.


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Additional Information

Nicolas Perrin
Affiliation: Mathematisches Institut, Heinrich-Heine-Universität, D-40225 Düsseldorf, Germany
Email: perrin@math.uni-duesseldorf.de

DOI: https://doi.org/10.1090/S0002-9947-2015-06279-5
Received by editor(s): July 2, 2013
Received by editor(s) in revised form: September 15, 2013
Published electronically: March 20, 2015
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.