Shunsuke.Tsuchioka

Affiliation: Institute of Science Tokyo

Title Of Talk: Schur partition theorems from the viewpoint of spin representations of the symmetric groups

URLS:
https://arxiv.org/abs/1609.01905

Abstract: Motivated by spin modular representations of the symmetric groups, we propose two generalizations of the Schur regular partitions for an odd integer $p\geq 3$. One forms a subset of the set of $p$-strict partitions, and the other forms that of strict partitions. We prove that each set has a basic $A^{(2)}_{p-1}$-crystal structure. For $p=3$, it reproves Schur's 1926 partition theorem, a mod 6 analog of the Rogers-Ramanujan partition theorem (RRPT). For $p=5$, it gives a computer-free proof of a conjecture by Andrews during his 3-parameter generalization of RRPT, which was first proved by Andrews-Bessenrodt-Olsson. This is a joint work with Masaki Watanabe.

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