Dual graded graphs for Kac–Moody algebras

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.

Locations

• Algebra & Number Theory - View - PDF
• Project Euclid (Cornell University) - View - PDF