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Polyhedral Realizations of Crystal Bases for Modified Quantum Algebras of Arbitrary Rank 2 Cases

Ayumu Hoshino
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Abstract

We describe the crystal bases of the modified quantum algebras and give the explicit form of the highest (or lowest) weight vector of its connected component $B_0(λ)$ containing the unit element for arbitrary rank 2 cases. We also present the explicit form of $B_0(λ)$ containing the highest (or lowest) weight vector by the polyhedral realization method.

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Ayumu Hoshino. 2004-03-11. Polyhedral Realizations of Crystal Bases for Modified Quantum Algebras of Arbitrary Rank 2 Cases. https://arxiv.org/abs/math/0403192

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