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2007 Dual graded graphs for Kac–Moody algebras
Thomas Lam, Mark Shimozono
Algebra Number Theory 1(4): 451-488 (2007). DOI: 10.2140/ant.2007.1.451

Abstract

Motivated by affine Schubert calculus, we construct a family of dual graded graphs (Γs,Γw) for an arbitrary Kac–Moody algebra g. The graded graphs have the Weyl group W of geh as vertex set and are labeled versions of the strong and weak orders of W respectively. Using a construction of Lusztig for quivers with an admissible automorphism, we define folded insertion for a Kac–Moody algebra and obtain Sagan–Worley shifted insertion from Robinson–Schensted insertion as a special case. Drawing on work of Proctor and Stembridge, we analyze the induced subgraphs of (Γs,Γw) which are distributive posets.

Citation

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Thomas Lam. Mark Shimozono. "Dual graded graphs for Kac–Moody algebras." Algebra Number Theory 1 (4) 451 - 488, 2007. https://doi.org/10.2140/ant.2007.1.451

Information

Received: 28 March 2007; Revised: 4 August 2007; Accepted: 1 September 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1200.05249
MathSciNet: MR2368957
Digital Object Identifier: 10.2140/ant.2007.1.451

Subjects:
Primary: 05E10
Secondary: 17B67, 57T15

Rights: Copyright © 2007 Mathematical Sciences Publishers

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