A Littelmann path model for crystals of generalized Kac-Moody algebras (Q1028355)

The authors extend the path model of \textit{P. Littelmann} [Invent. Math. 116, No. 1--3, 329--346 (1994; Zbl 0805.17019) and Ann. Math. (2) 142, No. 3, 499--525 (1995; Zbl 0858.17023)] to include imaginary simple roots. Instead of the Weyl group it is used a monoid with generators defined by the real and the imaginary simple roots. An isomorphism theorem and a character formula of Borcherds-Kac-Weyl type are proved for the crystals in the case of a not necessarily symmetrizable Borcherds-Cartan matrix.