# Rigged configurations and the $\ast$-involution for generalized Kac--Moody algebras

## TL;DR

This paper develops a uniform model for highest weight crystals of generalized Kac--Moody algebras using rigged configurations, and explicitly describes the $ ext{*}$-involution, enhancing understanding of their structure.

## Contribution

It introduces a new uniform model for crystals of generalized Kac--Moody algebras and explicitly characterizes the $ ext{*}$-involution on rigged configurations.

## Key findings

- Explicit description of the $ ext{*}$-involution interchanging rigging and corigging.
- Recognition theorem for $B( ext{infty})$ using the $ ext{*}$-involution.
- Characterization of $B( ext{infty})$ and $B( ext{lambda})$ as subcrystals.

## Abstract

We construct a uniform model for highest weight crystals and $B(\infty)$ for generalized Kac--Moody algebras using rigged configurations. We also show an explicit description of the $\ast$-involution on rigged configurations for $B(\infty)$: that the $\ast$-involution interchanges the rigging and the corigging. We do this by giving a recognition theorem for $B(\infty)$ using the $\ast$-involution. As a consequence, we also characterize $B(\lambda)$ as a subcrystal of $B(\infty)$ using the $\ast$-involution.