On the Kernel of the Borel’s Characteristic Map of Lie Groups

For compact and connected Lie group G with a maximal torus T the quotient space G/T is canonically a smooth projective manifold,known as the complete flag manifold of the group G.The cohomology ring map c^(∗):H^(∗)(B T)→H∗(G/T)induced by the inclusion c:G/T→B_(T) is called the Borel’s characteristic map of the group G[7,8],where B T denotes the classifying space of T.Let G be simply-connected and simple.Based on the Schubert presentation of the cohomology H^(∗)(G/T)of the flag manifold G/T obtained in[10,11],we develop a method to find a basic set of explicit generators for the kernel ker c^(∗)⊂H^(∗)(B_(T))of the characteristic map c.