Dual graded graphs for Kac-Moody algebras

Abstract

Motivated by affine Schubert calculus, we construct a family of dual graded graphs $({\Gamma }_s,{\Gamma }_w)$ 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 $({\Gamma }_s,{\Gamma }_w)$ which are distributive posets.

36 pages

Cited by in corpus (1)

• Quantum cohomology of G/P and homology of affine Grassmannian