Cohomology Homomorphisms between Certain Flag Manifolds

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CohomologyHomomorphismsbetweenCertainFlagManifolds∗
ZhaoXuAn
DepartmentofMathematics,BeijingNormalUniversity
Beijing100875,zhaoxa@bnu.edu.cn
Abstract
Inthispaper,weintroducesometoolstoclassifyhomomorphismsbetweencohomologyringsofflagmanifolds.Thesemethodsinclude(1Gr¨obnerbasisofthedefinitionidealofthecohomologyringofaflagmanifold.(2Heightfiltrationonthetwodimensionalcohomologygroupofaflagmanifold.Usethesetools,explicitclassificationofhomomorphismscanbeobtainedinsomecases.
1Introduction
LetGbeaconnectedcompactLiegroupandTafixedmaximaltorussubgroupsofG,thenG/TiscalledtheflagmanifoldofG.FortwoflagmanifoldsX=G/TandX

Cohomology Homomorphisms between Certain Flag Manifolds

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