(untitled) (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, 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 kerc^∗ ⊂ H^∗ (B_T) of the characteristic map c.