A Conjecture for the Applicability Condition of Jimbo's Method

Ma Zhongqi

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2024年10月30日

Chinese Physics C> 1992, Vol. 16> Issue(S1) : 57-64

A Conjecture for the Applicability Condition of Jimbo's Method

Ma Zhongqi

Institute of High Energy Physics, the Chinese Academy of Sciences, Beijing, China

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According to Jimbo's theorem, the method for constructing the spectrum-dependent solutions to the Yang-Baxter equation is based on the existence of the representation matrix of e₀ that corresponds to the lowest negative root, in an irreducible representation of a quantum enveloping algebra. This paper discusses a conjecture for the existence condition of the representation matrix of e₀. As an example, the adjoin representation of U_qC₂ is discussed where the representation matrix e₀ does not exist because the existence condition is violated.

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Ma Zhongqi. A Conjecture for the Applicability Condition of Jimbo's Method[J]. Chinese Physics C, 1992, 16(S1): 57-64.

Ma Zhongqi. A Conjecture for the Applicability Condition of Jimbo's Method[J]. Chinese Physics C, 1992, 16(S1): 57-64. shu

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Received: 1991-08-17

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Supported by the National Natural Science Foundation of China.

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A Conjecture for the Applicability Condition of Jimbo's Method

Ma Zhongqi

Institute of High Energy Physics, the Chinese Academy of Sciences, Beijing, China

Received Date: 1991-08-17

Fund Project: Supported by the National Natural Science Foundation of China.

Abstract: According to Jimbo's theorem, the method for constructing the spectrum-dependent solutions to the Yang-Baxter equation is based on the existence of the representation matrix of e₀ that corresponds to the lowest negative root, in an irreducible representation of a quantum enveloping algebra. This paper discusses a conjecture for the existence condition of the representation matrix of e₀. As an example, the adjoin representation of U_qC₂ is discussed where the representation matrix e₀ does not exist because the existence condition is violated.