Descriptions of the crystal $B(\infty)$ for $G_2$

Details Descriptions of the crystal $B(\infty)$ for $G_2$ Descriptions of the crystal $B(\infty)$ for $G_2$

2005-08-13

arxiv.org/abs/math/0508231v1

Mathematics

Quantum Algebra

18 pages

Scientific paper

We study the crystal base of the negative part of a quantum group. Two
explicit descriptions of the crystal $B(\infty)$ for types $G_2$ are given. The
first is given in terms of extended Nakajima monomials and the second
realization follows a similar result given for other finite types by Cliff.

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