Super RSK correspondence with symmetry

TL;DR

This paper introduces a new super RSK correspondence that generalizes the symmetry property to all cases, based on Haiman's mixed insertion process, improving upon previous limitations.

Contribution

It presents a novel super RSK bijection that ensures symmetry in all cases, unlike previous versions that only held in special situations.

Findings

New super RSK bijection with full symmetry

Based on Haiman's mixed insertion process

Generalizes classical symmetry property

Abstract

Super RSK correspondence is a bijective correspondence between superbiwords and pairs of semistandard supertableaux. Such a bijection was given by Bonetti, Senato and Venezia, via an insertion algorithm closely related to Schensted insertion. Notably, the symmetry property satisfied by the classical RSK bijection holds only in special cases under this bijection. We present a new super RSK bijection, based on the mixed insertion process defined by Haiman, where the symmetry property holds in complete generality.