Algebraization of Frobenius splitting via quantum groups. (English) Zbl 1078.14074

In this paper, using Lusztig’s Frobenius maps for quantum groups at roots of unity, the authors give a representation-theoretic proof of the Frobenius-split property of Schubert varieties in the generalized flag varieties. This paper makes an important contribution to the geometry and representation theory of flag varieties.


14M15 Grassmannians, Schubert varieties, flag manifolds
20G05 Representation theory for linear algebraic groups
17B37 Quantum groups (quantized enveloping algebras) and related deformations
20G10 Cohomology theory for linear algebraic groups
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