Dual graded graphs for Kac-Moody algebras
Thomas Lam, Mark Shimozono
Abstract
Motivated by affine Schubert calculus, we construct a family of dual graded graphs (Γs,Γw) for an arbitrary Kac-Moody algebra (A). The graded graphs have the Weyl group W of (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 (Γs,Γw) which are distributive posets.
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