NDLI: Chains in the Bruhat order

Content Provider	Springer Nature Link
Author	Postnikov, Alexander Stanley, Richard P.
Copyright Year	2008
Abstract	We study a family of polynomials whose values express degrees of Schubert varieties in the generalized complex flag manifold G/B. The polynomials are given by weighted sums over saturated chains in the Bruhat order. We derive several explicit formulas for these polynomials, and investigate their relations with Schubert polynomials, harmonic polynomials, Demazure characters, and generalized Littlewood-Richardson coefficients. In the second half of the paper, we study the classical flag manifold and discuss related combinatorial objects: flagged Schur polynomials, 312-avoiding permutations, generalized Gelfand-Tsetlin polytopes, the inverse Schubert-Kostka matrix, parking functions, and binary trees.
Starting Page	133
Ending Page	174
Page Count	42
File Format	PDF
ISSN	09259899
Journal	Journal of Algebraic Combinatorics
Volume Number	29
Issue Number	2
e-ISSN	15729192
Language	English
Publisher	Springer US
Publisher Date	2008-03-15
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Flag manifold Schubert varieties Bruhat order Saturated chains Harmonic polynomials Grothendieck ring Demazure modules Schubert polynomials Flagged Schur polynomials 312-avoiding permutations Kempf elements Vexillary permutations Gelfand-Tsetlin polytope Toric degeneration Parking functions Binary trees Group Theory and Generalizations Computer Science Order, Lattices, Ordered Algebraic Structures Convex and Discrete Geometry Combinatorics
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Algebra and Number Theory

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Chains in the Bruhat order

Chains in the Bruhat order

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Schubert polynomials as projections of Minkowski sums of Gelfand-Tsetlin polytopes

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