On the cohomology ring of the infinite flag manifold LG/T

Abstract

In this work, we discuss the calculation of cohomology rings of LG/T. First we describe the root, system and Weyl group of LG, then we give some homotopy equivalences on. the loop groups and homogeneous spaces, and investigate the cohomology ring structures of $LSU_2/T$ and $Omega SU_2$. Also we prove that BGG-type operators correspond to partial derivation operators on the divided power algebras.