The braid group surjects onto $G_2$ tensor space
Quantum Algebra
2011-02-24 v1 Representation Theory
Abstract
Let V be the 7-dimensional irreducible representation of the quantum group U_q(g_2). For each n, there is a map from the braid group B_n to the endomorphism algebra of the n-th tensor power of V, given by R-matrices. We can extend this linearly to a map on the braid group algebra. Lehrer and Zhang (MR2271576) prove this map is surjective, as a special case of a more general result. Using Kuperberg's spider for G_2 from arXiv:math.QA/9201302, we give an elementary diagrammatic proof of this result.
Cite
@article{arxiv.0907.0256,
title = {The braid group surjects onto $G_2$ tensor space},
author = {Scott Morrison},
journal= {arXiv preprint arXiv:0907.0256},
year = {2011}
}
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9 pages