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arXiv · 0907.0256

The braid group surjects onto $G_2$ tensor space

Scott Morrison
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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.

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Scott Morrison. 2009-07-01. The braid group surjects onto $G_2$ tensor space. https://doi.org/10.2140/pjm.2011.249.189

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