CJO - Abstract - A unified formula for Steenrod operations in flag manifolds

Compositio Mathematica (2007), 143 : 257-270 Cambridge University Press

Copyright © Foundation Compositio Mathematica 2007

doi:10.1112/S0010437X06002405

Published online by Cambridge University Press 19 Jan 2007

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A unified formula for Steenrod operations in flag manifolds

Haibao Duan ^a1 and Xuezhi Zhao ^a2
^a1 Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, People's Republic of China dhb@math.ac.cn
^a2 Department of Mathematics, Capital Normal University, Beijing 100037, People's Republic of China zhaoxve@mail.cnu.edu.cn

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duan h [Google Scholar]

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Abstract

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 $G$.

(Published Online January 19 2007)
(Received February 14 2005)
(Accepted May 10 2006)

Key Words: Steenrod operations; flag manifolds; Schubert cells; Cartan numbers.

Maths Classification

55S10; 14M10; 14M15.