Vol. 1, No. 4, 2007

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Dual graded graphs for Kac–Moody algebras

Thomas F. Lam and Mark Shimozono

Vol. 1 (2007), No. 4, 451–488

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.

dual graded graphs, Schensted insertion, affine insertion
Mathematical Subject Classification 2000
Primary: 05E10
Secondary: 57T15, 17B67
Received: 28 March 2007
Revised: 4 August 2007
Accepted: 1 September 2007
Published: 1 November 2007
Thomas F. Lam
Department of Mathematics
Harvard University
Cambridge MA 02138
Mark Shimozono
Department of Mathematics
Virginia Polytechnic Institute and State University
Blacksburg, VA 24061-0123