Solving for Root Subgroup Coordinates: The SU(2) Case
Group Theory
2015-09-22 v1 Representation Theory
Abstract
Previously we showed that a loop in a simply connected compact Lie group K has a unique triangular factorization if and only if the loop has a unique root subgroup factorization (relative to a choice of a reduced sequence of simple reflections in the affine Weyl group). In this paper we show that in the K=SU(2) case, root subgroup coordinates are rational functions (with positive denominators) of the triangular factorization coordinates. We conjecture that in general they are algebraic functions.
Keywords
Cite
@article{arxiv.1509.05947,
title = {Solving for Root Subgroup Coordinates: The SU(2) Case},
author = {Doug Pickrell},
journal= {arXiv preprint arXiv:1509.05947},
year = {2015}
}
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9 pages