An algebraic cell decomposition of the nonnegative part of a flag variety
K. Rietsch
Abstract
We study the nonnegative part B 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 0 has an algebraic cell decomposition indexed by pairs w w' of the Weyl group. This result was conjectired by Lusztig in [Lu; Progress in Math 123].
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