A Conjecture for the Effecture Condition of Jimbo's Method

MA Zhong-Qi

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2024年10月30日

Chinese Physics C> 1992, Vol. 16> Issue(4) : 352-358

A Conjecture for the Effecture Condition of Jimbo's Method

MA Zhong-Qi ^,

Institute of High Energy Physics,Academia Sinica,Beijing 100039

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Abstract：
The method for constructing the spectrum-dependent solutions to the Yang-Baxter equation,according to Jimbo's theorem,is based on the existence of the representation matrix of e₀,corresponding to the lowest negative root,in an irreducible representation of a quantum eveloping algebra.In this paper a conjecture for the existent condition of the representation matrix of e₀ is made.As an example,the adjoint representation of U_q C₂ is discussed where the representation matrix e₀ does not exist because the existent condition is violated.

References

[1]

M. Jimbo, Common. Math. Phys., 102(1986), 537.[2] Zhong-Qi Ma, Common, Theor, Phys., 15(1991), 37.[3] A. Kuniba, J. Phys., A23(1990), 1349; Zhong-Qi Ma, J. Phys., A24(1991), 433; Bo-Yuan Hou and Zhong-Qi Ma, J. Phys., A24(1991), 1363; BmYu Hou, Bo-Yuan Hou, Zhong-Qi Ma and Yu-Dong Yin, J. Moth.Phys., 32(1991), 2210; Bo-Yu Hou, Bo-Yuan Hou, Zhong-Qi Ma and Yu-Dong Yin, to appear in Mod.Phys. Lett.[4] M. Jimbo, Quantum R matrix related to the generalized Toda system: an algebraic approach, Lecture Notes on Physics, No. 246, p. 335.[5] 宋行长，1990年在中国高等科技中心(CCAST)关于量子群和共形场论工作月上的报告;Xing-ChangSong J. Phys, A23(1990),L821.[6] V. G. Drinfeld, Sov. Math. Dokl., 32(1985), 254.[7] M. Jimbo, Introduction to the Yang-Baxter equation, in "Braid Group, Knot Theory and Statistical Me-chanics" ed. by C. N. Yang and M. L. Ge, P. 111, World Scientific, Singapore, 1989.

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MA Zhong-Qi. A Conjecture for the Effecture Condition of Jimbo's Method[J]. Chinese Physics C, 1992, 16(4): 352-358.

MA Zhong-Qi. A Conjecture for the Effecture Condition of Jimbo's Method[J]. Chinese Physics C, 1992, 16(4): 352-358. shu

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Received: 1900-01-01
Revised: 1900-01-01

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A Conjecture for the Effecture Condition of Jimbo's Method

MA Zhong-Qi ^,

Corresponding author: MA Zhong-Qi,

Institute of High Energy Physics,Academia Sinica,Beijing 100039

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1992-04-05

Abstract: The method for constructing the spectrum-dependent solutions to the Yang-Baxter equation,according to Jimbo's theorem,is based on the existence of the representation matrix of e₀,corresponding to the lowest negative root,in an irreducible representation of a quantum eveloping algebra.In this paper a conjecture for the existent condition of the representation matrix of e₀ is made.As an example,the adjoint representation of U_q C₂ is discussed where the representation matrix e₀ does not exist because the existent condition is violated.