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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.

MSC:

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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