Polyhedral realization of Crystal bases for Generalized Kac-Moody Algebras

Mathematics – Quantum Algebra

Scientific paper

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20 pages

Scientific paper

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}.

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