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Algebraization of Frobenius splitting via quantum groups

Shrawan Kumar·Peter Littelmann
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Abstract

An important breakthrough in understanding the geometry of Schubert varieties was the introduction of the notion of Frobenius split varieties and the result that the flag varieties G/P are Frobenius split. The aim of this article is to give in this case a complete and self contained representation theoretic approach to this method. The geometric Frobenius method in (char k=p>0) will here be replaced by Lusztig's Frobenius maps for quantum groups at roots of unity (which exist not only for primes but any odd integer \ell >1).

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Shrawan Kumar, Peter Littelmann. 2004-05-20. Algebraization of Frobenius splitting via quantum groups. https://arxiv.org/abs/math/0005246

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