A Littelmann path model for crystals of generalized Kac–Moody algebras

Abstract

A Littelmann path model is constructed for crystals pertaining to a not necessarily symmetrizable Borcherds–Cartan matrix. Here one must overcome several combinatorial problems coming from the imaginary simple roots. The main results are an isomorphism theorem and a character formula of Borcherds–Kac–Weyl type for the crystals. In the symmetrizable case, the isomorphism theorem implies that the crystals constructed by this path model coincide with those of Jeong, Kang, Kashiwara and Shin obtained by taking q → 0 limit in the quantized enveloping algebra.