A Conjecture for the Applicability Condition of Jimbo's Method

Ma Zhongqi

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

Abstract
HTML
Reference
Related

PDF

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.

[1]	Ayan Banerjee , Indrani Karar , Javlon Rayimbaev , Inomjon Ibragimov , Sardor Murodov , Sokhibjan Muminov , Sardor Jumaniyozov . Existence of quark stars in gravity's Rainbow: the significance of strongly interacting quark matter. Chinese Physics C, 2026, 50(2): 1-12.
[2]	Li Tang , Liang Liu , Ying Wu . Null test of cosmic curvature using deep learning method. Chinese Physics C, 2026, 50(2): 1-8.
[3]	Wentao Zeng , Zehao Lin , Yiran Wang , Shuangquan Zhang , Jinniu Hu , Ying Zhang . Resonant states in the Schrödinger equation solved by the Green's function method. Chinese Physics C, 2026, 50(2): 1-10.
[4]	Xi-Liang Yuan , Chao Wang , Zhuang-Dong Bai , Gang Lü . Role and contribution of the resonance effect for the decay process of ${ \bar {\boldsymbol B}^{\bf 0}_{\boldsymbol s} \boldsymbol\rightarrow \boldsymbol\pi^{+}\boldsymbol\pi^{-}{\boldsymbol P}}$. Chinese Physics C, 2025, 49(11): 113103. doi: 10.1088/1674-1137/ade6d8
[5]	Muhammad Farhan Taseer , Subhash Singha . Impact of particle production mechanisms on pseudorapidity distribution and directed flow in Au+Au and Cu+Cu collisions at ${ \sqrt{{\boldsymbol s}_{\boldsymbol{ NN}}}}$ = 19.6 GeV using AMPT model. Chinese Physics C, 2025, 49(10): 104101. doi: 10.1088/1674-1137/ade660
[6]	Hao Yang , Zhi-Qing Zhang , You-Ya Yang , Peng Li . $ {{\boldsymbol D}^*_{ {({\boldsymbol s})}}{\bf\to} {\boldsymbol P} }$ form factors and their applications to semi-leptonic and non-leptonic weak decays. Chinese Physics C, 2025, 49(12): 123104. doi: 10.1088/1674-1137/adfb5d
[7]	Yingjie Fan , Xuewen Liu , Ning Zhou . Characterizing the CJPL’s site-specific neutrino floor as the neutrino fog boundary. Chinese Physics C, 2025, 49(10): 103001. doi: 10.1088/1674-1137/ade65e
[8]	Yu Xi , Fu-Wen Shu . Constraints on Lorentz invariance violation from GRB 221009A using the DisCan method. Chinese Physics C, 2025, 49(12): 125101. doi: 10.1088/1674-1137/adfa01
[9]	Xiaobin Wang , Lei Chang . Unveiling the inner structure of the Pion’s first excited state. Chinese Physics C, 2025, 49(12): 123107. doi: 10.1088/1674-1137/adfc34
[10]	Che-Hao Liu , Van Que Tran , Qiaoyi Wen , Fanrong Xu , Tzu-Chiang Yuan . New contributions to b → sγ in the minimal G2HDM. Chinese Physics C, 2025, 49(8): 083107. doi: 10.1088/1674-1137/add873
[11]	WANG Ji-Ke , MAO Ze-Pu , BIAN Jian-Ming , CAO Guo-Fu , CAO Xue-Xiang , CHEN Shen-Jian , DENG Zi-Yan , FU Cheng-Dong , GAO Yuan-Ning , HE Kang-Lin , HE Miao , HUA Chun-Fei , HUANG Bin , HUANG Xing-Tao , JI Xiao-Bin , LI Fei , LI Hai-Bo , LI Wei-Dong , LIANG Yu-Tie , LIU Chun-Xiu , LIU Huai-Min , LIU Suo , LIU Ying-Jie , MA Qiu-Mei , MA Xiang , MAO Ya-Jun , MO Xiao-Hu , PAN Ming-Hua , PANG Cai-Ying , PING Rong-Gang , QIN Ya-Hong , QIU Jin-Fa , SUN Sheng-Sen , SUN Yong-Zhao , WANG Liang-Liang , WEN Shuo-Pin , , , , , , . Software alignment of the BESⅢ main drift chamber using the Kalman Filter method. Chinese Physics C, 2009, 33(3): 210-216. doi: 10.1088/1674-1137/33/3/010
[12]	ZHANG Man-Zhou , HOU Jie , LI Hao-Hu , LIU Gui-Min , LI De-Ming . Optimal sorting method and application to SSRF booster dipoles. Chinese Physics C, 2008, 32(11): 924-927. doi: 10.1088/1674-1137/32/11/015
[13]	GUO Yun-Jun , HE Kang-Lin . Muon Identification Using the Efficiencies Ratio Method at BESⅡ. Chinese Physics C, 2007, 31(11): 1050-1055.
[14]	SHEN Shui-Fa , YU Xiao-Han . Decay of ⁸³Sr and Discussion of Its Daughter's Band Structures. Chinese Physics C, 2004, 28(S1): 78-80.
[15]	CHANG KONG-LIANG . DIMENSIONAL METHOD TO SOLVE THE DIFFUSION CONVECTION EQUATION OF SOLAR COSMIC RAYS. Chinese Physics C, 1978, 2(3): 200-210.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1991-08-17

Fund

Supported by the National Natural Science Foundation of China.

Article Metric

Article Views(1192)
PDF Downloads(2)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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.