On the Kernel of the Borel’s Characteristic Map of Lie Groups (Communications in Mathematical Research, 2023)
For compact and connected Lie group $G$ with a maximal torus $T$ the quotient space $G/T$ is canonically a smooth projective manifold, knownas 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 theBorel’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 Schubertpresentation of the cohomology $H^∗(G/T)$ of the flag manifold $G/T$ obtainedin $[10, 11],$ we develop a method to find a basic set of explicit generators for thekernel ker$c^∗ ⊂ H^∗(B_T)$ of the characteristic map $c.$