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arXiv · 1407.2964

Essential paths space on ADE SU(3) graphs: A geometric approach

Jesus A. Pineda·E. Isasi·M. I. Caicedo
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Abstract

For simply laced $SU(3)$ graphs we offer a geometric understanding of the path creation and annihilation operators for $SU(3)$ 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.

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Jesus A. Pineda, E. Isasi, M. I. Caicedo. 2014-07-10. Essential paths space on ADE SU(3) graphs: A geometric approach. https://arxiv.org/abs/1407.2964

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