Equivariant K-theory of compactifications of algebraic groups
Equivariant K-theory of compactifications of algebraic groups
复制标题
代数群紧化的等变K-理论
DOI：
10.1007/s00031-006-0042-3
复制
发表时间：
2005
影响因子：
0.7
通讯作者：
V. Uma
中科院分区：
文献类型：
--
作者：
V. Uma
本文描述了X的G × G-等变K-环，其中X是连通复约化代数群G的正则紧化.当G是伴随型半单群，X是其奇妙紧化时，我们刻画了G的普通K-环K（X）.更精确地说，我们证明了K（X）是K（G/B）上秩为Weyl群基数的自由模.我们进一步给出了K（X）在K（G/B）上的一个显式基，并确定了关于这个基的结构常数.
In this paper we describe the G × G-equivariant K-ring of X, where X is a regular compactification of a connected complex reductive algebraic group G. Furthermore, in the case when G is a semisimple group of adjoint type, and X its wonderful compactification, we describe its ordinary K-ring K(X). More precisely, we prove that K(X) is a free module over K(G/B) of rank the cardinality of the Weyl group. We further give an explicit basis of K(X) over K(G/B), and also determine the structure constants with respect to this basis.