Algebraization of Frobenius splitting via quantum groups

• 成果类型: Article
• 署名作者: Kumar, S; Littelmann, P
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3062124
• 发表日期: 2002
• 页码: 491-551
• 关键词: demazure character formula; schubert varieties; ALGEBRAS; REPRESENTATIONS; COHOMOLOGY; MODULES

摘要

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 GIP 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 Robenius maps for quantum groups at roots of unity (which exist not only for primes but any odd integer l > 1).