Split subvarieties of group embeddings

Perrin, Nicolas

doi:10.1090/S0002-9947-2015-06279-5

Split subvarieties of group embeddings
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Trans. Amer. Math. Soc. 367 (2015), 8421-8438 Request permission

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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