Perfect basis theory for quantum Borcherds-Bozec algebras

Abstract

In this paper, we develop the perfect basis theory for quantum Borcherds-Bozec algebras $U_q(\mathfrak{g})$ and their irreducible highest weight modules $V(\hat{I}»)$. We show that the lower perfect graph (resp. upper perfect graph) of every lower perfect basis (resp. upper perfect basis) of $U_q^{-}(\mathfrak{g})$ (resp. $V(\hat{I}»)$) is isomorphic to the crystal $B(\infty )$ (resp. $B(\hat{I}»)$).

arXiv admin note: text overlap with arXiv:2211.02859