Kumar, Shrawan; Littelmann, Peter Algebraization of Frobenius splitting via quantum groups. (English) Zbl 1078.14074 Ann. Math. (2) 155, No. 2, 491-551 (2002). 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. Reviewer: V. Lakshmibai (Boston) Cited in 1 ReviewCited in 12 Documents 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 Keywords:quantum groups; Frobenius PDFBibTeX XMLCite \textit{S. Kumar} and \textit{P. Littelmann}, Ann. Math. (2) 155, No. 2, 491--551 (2002; Zbl 1078.14074) Full Text: DOI arXiv