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UBC Theses and Dissertations

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UBC Theses and Dissertations

Bruhat decompositions and Schubert varieties Li, Qing

Abstract

This paper is divided into two parts. In first chapter we give a special C* action on G/ P and show that the associated plus decomposition of this action is the Bruhat decomposition of G/P. Moreover we prove that the set of Schubert varieties of Gk(Cⁿ) is in one to one correspondence with the plus cells of a certain C* action on Gk(Cⁿ). In chapter two we relate partitions to Schubert varieties. Also we relate the ordering of Schubert varieties by inclusion Gk(Cⁿ) to a quotient of the Bruhat ordering on the Weyl group Sn. Several examples have been included.

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