Murphy elements from the double-row transfer matrix
Mathematical Physics
2009-03-16 v3 High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
Abstract
We consider the double-row (open) transfer matrix constructed from generic tensor-type representations of various types of Hecke algebras. For different choices of boundary conditions for the relevant integrable lattice model we express the double-row transfer matrix solely in terms of generators of the corresponding Hecke algebra (tensor-type realizations). We then expand the open transfer matrix and extract the associated Murphy elements from the first/last terms of the expansion. Suitable combinations of the Murphy elements as has been shown commute with the corresponding Hecke algebra.
Cite
@article{arxiv.0812.0898,
title = {Murphy elements from the double-row transfer matrix},
author = {Anastasia Doikou},
journal= {arXiv preprint arXiv:0812.0898},
year = {2009}
}
Comments
12 pages, Latex. Clarifications and references added. To appear in JSTAT