an:05529315
Zbl 1200.05249
Lam, Thomas F.; Shimozono, Mark
Dual graded graphs for Kac-Moody algebras
EN
Algebra Number Theory 1, No. 4, 451-488 (2007).
00247149
2007
j
05E10 57T15 17B67 57M15
dual graded graphs; Robinson-Schensted insertion; Sagan-Worley insertion; affine insertion
Summary: Motivated by affine Schubert calculus, we construct a family of dual graded graphs \((\Gamma_s,\Gamma_w)\)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 \((\Gamma_s,\Gamma_w)\) which are distributive posets.