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arXiv · 1812.07746

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

Ben Salisbury·Travis Scrimshaw
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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 $B(λ)$ as a subcrystal of $B(\infty)$ using the $\ast$-involution.

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Ben Salisbury, Travis Scrimshaw. 2020-06-06. Rigged configurations and the $\ast$-involution for generalized Kac--Moody algebras. https://doi.org/10.1016/j.jalgebra.2020.12.035

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