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

1997/09/30 by Rietsch, K. · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9709035

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].

Cited by

• Totally nonnegative Peterson variety and strongly dominant weight polytope
• Positivity and Non-commutativity

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