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

Source: [An algebraic cell decomposition of the nonnegative part of a flag variety](<https://www.sota2.com/research/paper/68fa531b1e209131ce9807d4>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T12:16:06.364Z

Authors: K. Rietsch

Published: 1997-09-30T19:28:27.000Z

## Abstract

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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/alg-geom/9709035>)

[PDF](<https://arxiv.org/pdf/alg-geom/9709035.pdf>)