dorsal/arxiv
View SchemaSolutions of Discretized Affine Toda Field Equations for A_{n}^{(1)}, B_{n}^{(1)}, C_{n}^{(1)}, D_{n}^{(1)}, A_{n}^{(2)} and D_{n+1}^{(2)}
| Authors | Zengo Tsuboi |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9610011 |
| URL | https://arxiv.org/abs/solv-int/9610011 |
| DOI | 10.1143/JPSJ.66.3391 |
| Journal | J.Phys.Soc.Jap. 66 (1997) 3391-3398 |
Abstract
It is known that a family of transfer matrix functional equations, the T-system, can be compactly written in terms of the Cartan matrix of a simple Lie algebra. We formally replace this Cartan matrix of a simple Lie algebra with that of an affine Lie algebra, and then we obtain a system of functional equations different from the T-system. It may be viewed as an X_{n}^{(a)} type affine Toda field equation on discrete space time. We present, for A_{n}^{(1)}, B_{n}^{(1)}, C_{n}^{(1)}, D_{n}^{(1)}, A_{n}^{(2)} and D_{n+1}^{(2)}, its solutions in terms of determinants or Pfaffians.
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"abstract": "It is known that a family of transfer matrix functional equations, the\nT-system, can be compactly written in terms of the Cartan matrix of a simple\nLie algebra. We formally replace this Cartan matrix of a simple Lie algebra\nwith that of an affine Lie algebra, and then we obtain a system of functional\nequations different from the T-system. It may be viewed as an X_{n}^{(a)} type\naffine Toda field equation on discrete space time. We present, for A_{n}^{(1)},\nB_{n}^{(1)}, C_{n}^{(1)}, D_{n}^{(1)}, A_{n}^{(2)} and D_{n+1}^{(2)}, its\nsolutions in terms of determinants or Pfaffians.",
"arxiv_id": "solv-int/9610011",
"authors": [
"Zengo Tsuboi"
],
"categories": [
"solv-int",
"hep-th",
"nlin.SI"
],
"doi": "10.1143/JPSJ.66.3391",
"journal_ref": "J.Phys.Soc.Jap. 66 (1997) 3391-3398",
"title": "Solutions of Discretized Affine Toda Field Equations for A_{n}^{(1)}, B_{n}^{(1)}, C_{n}^{(1)}, D_{n}^{(1)}, A_{n}^{(2)} and D_{n+1}^{(2)}",
"url": "https://arxiv.org/abs/solv-int/9610011"
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