Polyhedral Realizations of Crystal Bases for Integrable Highest Weight Modules

Details Polyhedral Realizations of Crystal Bases for Integrable Highest Weight Modules Polyhedral Realizations of Crystal Bases for Integrable Highest Weight Modules

1998-06-16

arxiv.org/abs/math/9806085v2

Mathematics

Quantum Algebra

LaTeX, 27 pages, some reference is added

Scientific paper

We give a general way of representing the crystal (base) corresponding to the
intgrable highest weight modules of quantum Kac-Moody algebras, which is called
polyhedral realizations. This is applied to describe explicitly the crystal
bases of integrable highest weight modules for arbitrary rank 2 Kac-Moody
algebra cases, the classical A_n-case and the affine A^{(1)}_{n-1}-case.

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