TY - JOUR
T1 - Calogero-Moser models. III
T2 - Elliptic potentials and twisting
AU - Bordner, Andrew J.
AU - Sasaki, Ryu
PY - 1999/4
Y1 - 1999/4
N2 - Universal Lax pairs of the root type with spectral parameter and independent coupling constants for twisted non-simply laced Calogero-Moser models are constructed. Together with the Lax pairs for the simply laced models and untwisted non-simply laced models presented in two previous papers, this completes the derivation of universal Lax pairs for all of the Calogero-Moser models based on root systems. As for the twisted models based on Bn, Cn and BCn root systems, a new type of potential term with independent coupling constants can be added without destroying integrability. They are called extended twisted models. All of the Lax pairs for the twisted models presented here are new, except for the one for the F4 model based on the short roots. The Lax pairs for the twisted G2 model have some novel features. Derivation of various functions, twisted and untwisted, appearing in the Lax pairs for elliptic potentials with the spectral parameter is provided. The origin of the spectral parameter is also naturally explained. The Lax pairs with spectral parameter, twisted and untwisted, for the hyperbolic, the trigonometric and the rational potential models are obtained as degenerate limits of those for the elliptic potential models.
AB - Universal Lax pairs of the root type with spectral parameter and independent coupling constants for twisted non-simply laced Calogero-Moser models are constructed. Together with the Lax pairs for the simply laced models and untwisted non-simply laced models presented in two previous papers, this completes the derivation of universal Lax pairs for all of the Calogero-Moser models based on root systems. As for the twisted models based on Bn, Cn and BCn root systems, a new type of potential term with independent coupling constants can be added without destroying integrability. They are called extended twisted models. All of the Lax pairs for the twisted models presented here are new, except for the one for the F4 model based on the short roots. The Lax pairs for the twisted G2 model have some novel features. Derivation of various functions, twisted and untwisted, appearing in the Lax pairs for elliptic potentials with the spectral parameter is provided. The origin of the spectral parameter is also naturally explained. The Lax pairs with spectral parameter, twisted and untwisted, for the hyperbolic, the trigonometric and the rational potential models are obtained as degenerate limits of those for the elliptic potential models.
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U2 - 10.1143/PTP.101.799
DO - 10.1143/PTP.101.799
M3 - Article
AN - SCOPUS:0033112593
SN - 0033-068X
VL - 101
SP - 799
EP - 829
JO - Progress of Theoretical Physics
JF - Progress of Theoretical Physics
IS - 4
ER -