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

Ayumu Hoshino·Toshiki Nakashima
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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 A_n and A^(1)_1. We also present the explicit form of the unique highest weight vector in the connected component.

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Ayumu Hoshino, Toshiki Nakashima. 2004-01-09. Polyhedral Realizations of Crystal Bases for Modified Quantum Algebras of Type A. https://arxiv.org/abs/math/0401087

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