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

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

2004-03-11

arxiv.org/abs/math/0403192v1

Mathematics

Quantum Algebra

26 pages, LaTeX

Scientific paper

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 $B_0(\lambda)$ containing the unit element for arbitrary rank 2
cases. We also present the explicit form of $B_0(\lambda)$ containing the
highest (or lowest) weight vector by the polyhedral realization method.

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