SL(3,C)的Bernstein-Gelfand-Gelfand复形与Kasparov理论
算子代数
2009-11-13 v3 K理论与同调
摘要
设G=SL(3,ℂ)。我们从G的Bernstein-Gelfand-Gelfand复形构造了一个G-等变K-同调元素。这为从Kasparov表示环R(G)到其极大紧子群K的表示环R(K)的限制映射提供了一个显式分裂，且该分裂通过G的旗簇的等变K-同调。特别地，我们得到了G的γ元素的新模型。证明大量使用了作者此前关于旗簇上纵向伪微分算子调和分析的结果。
引用
@article{arxiv.0802.2094,
title = {The Bernstein-Gelfand-Gelfand complex and Kasparov theory for SL(3,C)},
author = {Robert Yuncken},
journal= {arXiv preprint arXiv:0802.2094},
year = {2009}
}
备注
Complete rewrite. Paper has been rewritten to take advantage of the paper "Products of Longitudinal Pseudodifferential Operators on Flag Varieties" (at http://dx.doi.org/10.1016/j.jfa.2009.10.007). Also added a result concerning order zero longitudinal pseudodifferential operators tangent to the fibrations of the flag variety of SL(3,C) -- Theorem 3.18