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      Jones-Wenzl idempotents For Rank 2 Simple Lie algebras

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          Abstract

          Temperley-Lieb algebras have been generalized to web spaces for rank 2 simple Lie algebras. Using these webs, we find a complete description of the Jones-Wenzl idempotents for the quantum sl(3) and sp(4) by single clasp expansions. We discuss applications of these expansions.

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          A polynomial invariant for knots via von Neumann algebras

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            Introduction to Lie Algebras and Representation Theory

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              Spiders for rank 2 Lie algebras

              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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                Author and article information

                Journal
                22 February 2006
                2011-05-03
                Article
                math/0602504
                338a7029-1388-4527-96b3-a1cf0179d059

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                Primary 57M27, Secondary 57M25, 57R56
                Osaka J. Math. 44(3) (2007), 691-722
                math.GN math.QA

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