# 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 $\ell>1$).

Shrawan Kumar

Peter Littelmann