Boundary remnant of Yangian symmetry and the structure of rational reflection matrices

G.W. Delius; N.J. MacKay; Ben Short

doi:10.1016/S0370-2693(01)01275-8

Boundary remnant of Yangian symmetry and the structure of rational reflection matrices

G.W. Delius, N.J. MacKay, Ben Short

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For the classical principal chiral model with boundary, we give the subset of the Yangian charges which remains conserved under certain integrable boundary conditions, and extract them from the monodromy matrix. Quantized versions of these charges are used to deduce the structure of rational solutions of the reflection equation, analogous to the ‘tensor product graph’ for solutions of the Yang–Baxter equation. We give a variety of such solutions, including some for reflection from non-trivial boundary states, for the SU(N) case, and confirm these by constructing them by fusion from the basic solutions.

Original language	English
Pages (from-to)	335-344
Number of pages	9
Journal	Physics Letters B
Volume	522
Issue number	3-4
DOIs	https://doi.org/10.1016/S0370-2693(01)01275-8
Publication status	Published - 13 Dec 2001

Keywords

IRREDUCIBLE REPRESENTATIONS
FUSION

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10.1016/S0370-2693(01)01275-8

http://dx.doi.org/10.1016/S0370-2693(01)01275-8

Cite this

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abstract = "For the classical principal chiral model with boundary, we give the subset of the Yangian charges which remains conserved under certain integrable boundary conditions, and extract them from the monodromy matrix. Quantized versions of these charges are used to deduce the structure of rational solutions of the reflection equation, analogous to the {\textquoteleft}tensor product graph{\textquoteright} for solutions of the Yang–Baxter equation. We give a variety of such solutions, including some for reflection from non-trivial boundary states, for the SU(N) case, and confirm these by constructing them by fusion from the basic solutions.",

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AU - Short, Ben

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N2 - For the classical principal chiral model with boundary, we give the subset of the Yangian charges which remains conserved under certain integrable boundary conditions, and extract them from the monodromy matrix. Quantized versions of these charges are used to deduce the structure of rational solutions of the reflection equation, analogous to the ‘tensor product graph’ for solutions of the Yang–Baxter equation. We give a variety of such solutions, including some for reflection from non-trivial boundary states, for the SU(N) case, and confirm these by constructing them by fusion from the basic solutions.

AB - For the classical principal chiral model with boundary, we give the subset of the Yangian charges which remains conserved under certain integrable boundary conditions, and extract them from the monodromy matrix. Quantized versions of these charges are used to deduce the structure of rational solutions of the reflection equation, analogous to the ‘tensor product graph’ for solutions of the Yang–Baxter equation. We give a variety of such solutions, including some for reflection from non-trivial boundary states, for the SU(N) case, and confirm these by constructing them by fusion from the basic solutions.

KW - IRREDUCIBLE REPRESENTATIONS

KW - FUSION

U2 - 10.1016/S0370-2693(01)01275-8

DO - 10.1016/S0370-2693(01)01275-8

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JF - Physics Letters B

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