Room 217

A Representation Theory Connection of the Schützenberger involution

Digjoy Paul

IMSc

The Schützenberger involution is a shape-preserving bijection on the set of semistandard Young tableaux. Its fixed points are known as self-evacuating tableaux.

We describe a nice bijection from the set of self-evacuating standard tableaux onto the set of standard bitableaux. It is well-known that standard bitableaux play the role of standard tableaux in the representation theory of hyperoctahedral groups.

In this context we generalize the RSK correspondence and a lemma of Schützenberger (relating the number of fixed points of an involution and the shape of the corresponding tableau) to hyperoctahedral groups. We use this to study Gelfand models for hyperoctahedral groups.