## Algebra & Number Theory

### 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.

#### Article information

Source
Algebra Number Theory, Volume 1, Number 4 (2007), 451-488.

Dates
Revised: 4 August 2007
Accepted: 1 September 2007
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513797171

Digital Object Identifier
doi:10.2140/ant.2007.1.451

Mathematical Reviews number (MathSciNet)
MR2368957

Zentralblatt MATH identifier
1200.05249

#### Citation

Lam, Thomas; Shimozono, Mark. Dual graded graphs for Kac–Moody algebras. Algebra Number Theory 1 (2007), no. 4, 451--488. doi:10.2140/ant.2007.1.451. https://projecteuclid.org/euclid.ant/1513797171

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