Graphical Calculus on Representations of Quantum Lie Algebras
Quantum Algebra
2007-05-23 v1 Representation Theory
Abstract
We develop graphical calculation methods. Jones-Wenzl projectors for U_q(sl(2,C)) are very powerful tools to find not only invariants of links but also invariants of 3-manifolds. We find single clasp expansions of generalized Jones-Wenzl projectors for simple Lie algebras of rank 2. Trihedron coefficients of the representation theory for U_q(sl(2,C)) has significant meaning and it is called 3j symbols. Using single clasp expansions for U_q(sl(3,C)), we find some trihedron coefficients of the representation theory of U_q(sl(3,C)). We study representation theory for U_q(sl(4,C)). We conjecture a complete set of relations for U_q(sl(4,C)).
Cite
@article{arxiv.math/0310143,
title = {Graphical Calculus on Representations of Quantum Lie Algebras},
author = {Dongseok Kim},
journal= {arXiv preprint arXiv:math/0310143},
year = {2007}
}
Comments
Dissertation for degree awarded March, 2003 from UC Davis, 63 pages