TY - JOUR
T1 - On the Kernel of the Borel’s Characteristic Map of Lie Groups
AU - Duan , Haibao
AU - Zhao , Xuezhi
JO - Communications in Mathematical Research 
VL - 2
SP - 173
EP - 189
PY - 2023
DA - 2023/04
SN - 39
DO - http://doi.org/10.4208/cmr.2022-0041
UR - https://global-sci.org/intro/article_detail/cmr/21543.html
KW - Lie group, flag manifold, Schubert calculus.
AB - <p style="text-align: justify;">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 $c.$</p>