An algebraic cell decomposition of the nonnegative part of a flag variety
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].
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.