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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 l > 1).

Algebraization of Frobenius Splitting via Quantum Groups