Year: 2023
Author: Haibao Duan, Xuezhi Zhao
Communications in Mathematical Research , Vol. 39 (2023), Iss. 2 : pp. 173–189
Abstract
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 $c.$
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2022-0041
Communications in Mathematical Research , Vol. 39 (2023), Iss. 2 : pp. 173–189
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Lie group flag manifold Schubert calculus.