Decorated Geometric Crystals, Polyhedral and Monomial Realizations of Crystal Bases

Details Decorated Geometric Crystals, Polyhedral and Monomial Realizations of Crystal Bases Decorated Geometric Crystals, Polyhedral and Monomial Realizations of Crystal Bases

2012-03-09

arxiv.org/abs/1203.2112v1

Mathematics

Quantum Algebra

18 pages

Scientific paper

We shall show that for type $A_n$ the realization of crystal bases obtained
from the decorated geometric crystals intorduced by Berenstein and Kazhdan
coincides with our polyhedral realizations of crystal bases. We also observe
certain relations of decorations and monomial realizations of crystal bases.

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