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

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

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.

Author Details

Haibao Duan

Xuezhi Zhao