Oscillating tableaux and a superanalogue of the Robinson-Schensted-Knuth correspondence

In this paper, we investigate the super RSK correspondence, first introduced by Pak and Postnikov (1994), which generalizes both the RSK correspondence and the dual RSK correspondence. The bijection relates objects that are known as oscillating supertableau and (intransitive) supergraphs. We prove a number of theorems that were stated in the original paper of Pak and Postnikov, but whose proofs are missing in the literature. We also prove a generalized Cauchy identity associated to the super RSK correspondence. We believe this idea will lead to the notion of a super Schur process, generalizing the Schur process of Okounkov and Reshetikhin (2003).