Rigged configurations and the $*$-involution

TL;DR

This paper provides an explicit description of the $*$-involution within the rigged configuration model for the crystal basis $B( olinebreak( olinebreak) olinebreak ext{infinity})$, enhancing understanding of its algebraic structure.

Contribution

It introduces a clear, explicit characterization of the $*$-involution on rigged configurations, a key combinatorial model in representation theory.

Findings

Explicit formula for the $*$-involution on rigged configurations.

Improved understanding of the algebraic structure of $B( ext{infinity})$.

Potential applications in crystal basis theory and combinatorial representation theory.

Abstract

We give an explicit description of the $*$-involution on the rigged configuration model for $B(\infty)$.