2000/05/31 by Shrawan Kumar, Peter Littelmann
Mathematics · #math.QA #math.AG
published as Ann. of Math. (2), Vol. 155 (2002), no. 2, 491--551 · 62 pages, published version
arxiv created 2004/05/20 · arxiv updated 2009/11/30
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).