Séminaire Lotharingien de Combinatoire, 89B.74 (2023), 12 pp.

Jesse Kim

An Embedding of the Skein Action on Set Partitions into the Skein Action on Matchings

Abstract. Rhoades defined a skein action of the symmetric group on noncrossing set partitions which generalized an action of the symmetric group on matchings. The S_n-action on matchings is made possible via the Ptolemy relation, while the action on set partitions is defined in terms of a set of skein relations that generalize the Ptolemy relation. The skein action on noncrossing set partitions has seen applications to coinvariant theory and coordinate rings of partial flag varieties. We will show how Rhoades' S_n-module can be embedded into the S_n-module generated by matchings, thereby explaining how Rhoades' generalized skein relations all arise from the Ptolemy relation.

Received: November 15, 2022. Accepted: February 20, 2023. Final version: April 1, 2023.

The following versions are available:

PDF (211 K)
TeX version