Algebra & Number Theory

Dual graded graphs for Kac–Moody algebras

Thomas Lam and Mark Shimozono

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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
Received: 28 March 2007
Revised: 4 August 2007
Accepted: 1 September 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
Primary: 05E10: Combinatorial aspects of representation theory [See also 20C30]
Secondary: 57T15: Homology and cohomology of homogeneous spaces of Lie groups 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras

Keywords
dual graded graphs Schensted insertion affine insertion

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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