Split subvarieties of group embeddings

2013/07/02 by Nicolas Perrin, Perrin, Nicolas
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.AG #math.GR #math.RT

paper · pdf · doi:10.48550/arxiv.1307.0639

17 pages

arxiv created 2013/07/02 · arxiv updated 2013/07/03

Abstract

Let G be a connected reductive group and X an equivariant compactifiction of G. In X, we study generalised and opposite generalised Schubert varieties, 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.

Related

• Frobenius splitting and geometry of G-Schubert varieties
• On the B-canonical splittings of flag varieties
• Projections of Richardson Varieties
• Richardson Varieties and Equivariant K-Theory
• Frobenius split subvarieties pull back in almost all characteristics