Kronecker Comultiplication of Stable Characters and Restriction From $S_{mn}$ to $S_m\times S_n$

Abstract

A family of symmetric functions ${\tilde{s}}_{\lambda }$ was introduced in [OZ], and independently in [AS]. The ${\tilde{s}}_{\lambda }$ encode many stability properties of representations of symmetric groups (e.g. when multiplied, the structure constants are reduced Kronecker coefficients). We show that the structure constants for the Kronecker comultiplication ${\Delta }^{\ast }$ are multiplicities for the restriction of irreducible representations from $S_{mn}$ to $S_m\times S_n$ (provided $m$ and $n$ are sufficiently large), and use the structure of ${\tilde{s}}_{\lambda }$ to demonstrate two-row stability properties of these restriction multiplicities.

12 pages

References in corpus (2)

• GL-equivariant modules over polynomial rings in infinitely many variables
• Stability patterns in representation theory