An algebraic cell decomposition of the nonnegative part of a flag variety

Details An algebraic cell decomposition of the nonnegative part of a flag variety An algebraic cell decomposition of the nonnegative part of a flag variety

1997-09-30

arxiv.org/abs/alg-geom/9709035v1

Mathematics

Algebraic Geometry

9pp., AMSTeX

Scientific paper

We study the nonnegative part B_{\ge 0} of the flag variety of a reductive
algebraic group G, as defined by Lusztig. Using positivity properties of the
canonical basis it is shown that B_{\ge 0} has an algebraic cell decomposition
indexed by pairs w\le w' of the Weyl group. This result was conjectired by
Lusztig in [Lu; Progress in Math 123].

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