Skip to Main content Skip to Navigation
Conference papers

Type $A$ molecules are Kazhdan-Lusztig

Abstract : Let $(W, S)$ be a Coxeter system. A $W$-graph is an encoding of a representation of the corresponding Iwahori-Hecke algebra. Especially important examples include the $W$-graph corresponding to the action of the Iwahori-Hecke algebra on the Kazhdan-Lusztig basis as well as this graph's strongly connected components (cells). In 2008, Stembridge identified some common features of the Kazhdan-Lusztig graphs ("admissibility'') and gave combinatorial rules for detecting admissible $W$-graphs. He conjectured, and checked up to $n=9$, that all admissible $A_n$-cells are Kazhdan-Lusztig cells. The current paper provides a possible first step toward a proof of the conjecture. More concretely, we prove that the connected subgraphs of $A_n$-cells consisting of simple (i.e. directed both ways) edges do fit into the Kazhdan-Lusztig cells.
Document type :
Conference papers
Complete list of metadata

Cited literature [5 references]  Display  Hide  Download
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:20:58 AM
Last modification on : Wednesday, August 7, 2019 - 2:34:16 PM
Long-term archiving on: : Friday, April 28, 2017 - 9:56:44 PM


Publisher files allowed on an open archive


  • HAL Id : hal-01229745, version 1



Michael Chmutov. Type $A$ molecules are Kazhdan-Lusztig. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.313-324. ⟨hal-01229745⟩



Record views


Files downloads