Dual graded graphs for Kac-Moody algebras

2007/02/05 by Thomas Lam, Mark Shimozono, Lam, Thomas +1
Mathematics · #05E10 #17B67 #57T15 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.CO #math.RT #msc:05E10 #msc:17B67 #msc:57T15

paper · pdf · doi:10.48550/arxiv.math/0702090

36 pages

arxiv created 2007/10/01 · arxiv updated 2009/12/01

Abstract

Motivated by affine Schubert calculus, we construct a family of dual graded graphs (Γ_s,Γ_w) for an arbitrary Kac-Moody algebra \g(A). The graded graphs have the Weyl group W of \g(A) 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 Stembridge, we analyze the induced subgraphs of (Γ_s,Γ_w) which are distributive posets.

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