Spiders for rank 2 Lie algebras

Details Spiders for rank 2 Lie algebras Spiders for rank 2 Lie algebras

1997-11-29

arxiv.org/abs/q-alg/9712003v1

Comm. Math. Phys. 180(1):109-151, 1996

Mathematics

Combinatorics

33 pages. Has color figures

Scientific paper

A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or group-like object. We define certain combinatorial spiders by generators and relations that are isomorphic to the representation theories of the three rank two simple Lie algebras, namely A2, B2, and G2. They generalize the widely-used Temperley-Lieb spider for A1. Among other things, they yield bases for invariant spaces which are probably related to Lusztig's canonical bases, and they are useful for computing quantities such as generalized 6j-symbols and quantum link invariants.

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