Rigged configurations and the ⁎-involution for generalized Kac–Moody algebras

B. Salisbury, T. Scrimshaw

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish
Pages (from-to)148-168
Number of pages21
JournalJournal of Algebra
StatePublished - May 1 2021


  • Borcherds algebra
  • Crystal
  • Rigged configuration
  • ⁎-involution


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