Polyhedral realization of Crystal bases for Generalized Kac-Moody Algebras

Abstract

In this paper, we give polyhedral realization of the crystal $B(\infty)$ of $U_q^-(\mathfrak g)$ for the generalized Kac-Moody algebras. As applications, we give explicit descriptions of crystals for the generalized Kac-Moody algebras of rank 2, 3 and {\it Monster Lie algebras}.Comment: 20 page