| Project/Area Number |
16340033
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
JIMBO Michio The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (80109082)
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| Co-Investigator(Kenkyū-buntansha) |
MIWA Tetsuji Kyoto University, Department of Mathematics, Professor, 大学院・理学研究科, 教授 (10027386)
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| Project Period (FY) |
2004 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥6,800,000 (Direct Cost: ¥6,800,000)
Fiscal Year 2005: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2004: ¥4,400,000 (Direct Cost: ¥4,400,000)
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| Keywords | correlation function / spin chain / qKZ equation / XXZ model / Virasoro algebra / monomial basis / XXZ模型 / Virasoro代数 / 単項基底 / 相関関数 / qKZ方程式 / XXX模型 / 形状因子 |
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| Research Abstract |
1.Algebraic representation of correlation functions
We obtained an algebraic representation for correlation functions of integrable XXX, XXZ spin chains in which use of multiple integrals is avoided. A similar conjectural formula is also found for the -XYZ chain. The previous formula, obtained through our researches in the last year, is improved to a form applicable to physically important homogeneous chains. For quantum group invariant operators in the XXZ chain only one transcendental function is involved.
2.Monomial basis in conformal field theory
We studied the Virasoro minimal modules M(p, p') with 1 < p'/p < 2.We constructed a monomial basis using the Fourier components of the (2, 1)-primary field, and determined their quadratic relations. We also found conjectural bases in the case p'/p > 2, and for 1 < p'/p <2 using (1, 3)-primary field, and showed that their numbers match the character of the representation space. In the latter case with p'= p + 1 the character is shown to coincide with that of the fusion product of two sl_2-modules.
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