Essential paths space on ADE SU(3) graphs: A geometric approach
Mathematical Physics
2015-04-14 v2 math.MP
Abstract
For simply laced graphs we offer a geometric understanding of the path creation and annihilation operators for in terms of creation and annihilation of sequences of three vertices forming triangular cells or collapsed triangular cells. We prove that the space of paths of a given length can be decomposed as a direct sum of orthogonal sub-spaces constructed by recurrent applications of the path creation operator on subspaces of essential paths of shorter length.
Cite
@article{arxiv.1407.2964,
title = {Essential paths space on ADE SU(3) graphs: A geometric approach},
author = {Jesus A. Pineda and E. Isasi and M. I. Caicedo},
journal= {arXiv preprint arXiv:1407.2964},
year = {2015}
}
Comments
12 pages, 4 figures, v2: revised length with a more formal mathematical structure. Some partial results have been removed for clarity