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

Ayumu Hoshino

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

Quantum Algebra 2007-05-23 v1 Representation Theory

Authors: Ayumu Hoshino

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 $B_0(\lambda)$ 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.

Keywords

crystal bases modified quantum algebras polyhedral realization rank 2 highest weight vector connected component

Cite

@article{arxiv.math/0403192,
  title  = {Polyhedral Realizations of Crystal Bases for Modified Quantum Algebras of Arbitrary Rank 2 Cases},
  author = {Ayumu Hoshino},
  journal= {arXiv preprint arXiv:math/0403192},
  year   = {2007}
}

Comments

26 pages, LaTeX

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