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A unified formula for Steenrod operations in flag manifolds

Published online by Cambridge University Press:  19 January 2007

Haibao Duan  and
Xuezhi Zhao
Haibao Duan
Affiliation:
Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, People's Republic of Chinadhb@math.ac.cn
Xuezhi Zhao
Affiliation:
Department of Mathematics, Capital Normal University, Beijing 100037, People's Republic of Chinazhaoxve@mail.cnu.edu.cn
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Abstract

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The classical Schubert cells on a flag manifold $G/P$ give a cell decomposition for $G/P$ whose Kronecker duals (known as Schubert classes) form an additive base for the integral cohomology $H^{\ast}(G/P)$. We present a formula that expresses Steenrod mod-$p$ operations on Schubert classes in $G/P$ in terms of Cartan numbers of $G$.

Keywords

Steenrod operationsflag manifoldsSchubert cellsCartan numbers55S1014M1014M15
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 1 , January 2007 , pp. 257 - 270
Copyright
Foundation Compositio Mathematica 2007