Murphy elements from the double-row transfer matrix

Details Murphy elements from the double-row transfer matrix Murphy elements from the double-row transfer matrix

2008-12-04

arxiv.org/abs/0812.0898v3

J. Stat. Mech. (2009) L03003

Physics

Mathematical Physics

12 pages, Latex. Clarifications and references added. To appear in JSTAT

Scientific paper

10.1088/1742-5468/2009/03/L03003

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.

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