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Polyhedral Realizations of Crystal Bases for Modified Quantum Algebras of Type A

Ayumu Hoshino, Toshiki Nakashima

math.QAarXiv:math/0401087

Abstract

We describe the crystal bases of modified quantum algebras and its connected component containing ``zero vector''by the polyhedral realization method for the types An and A(1)1. We also present the explicit form of the unique highest weight vector in the connected component.

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