Abstract
Motivated by affine Schubert calculus, we construct a family of dual graded graphs for an arbitrary Kac–Moody algebra . The graded graphs have the Weyl group of as vertex set and are labeled versions of the strong and weak orders of 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 which are distributive posets.
Citation
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
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