Algebraization of Frobenius splitting via quantum groups

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 $\ell>1$).

DOI
http://doi.org/10.2307/3062124

Authors

Shrawan Kumar

Peter Littelmann