• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Representation theory of elliptic quantum groups and its application

Research Project

Project/Area Number 11640030
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHiroshima University

Principal Investigator

KONNO Hitoshi  Hiroshima Univ., Fac. of Integrated Arts & Sci. Assoc., Prof., 総合科学部, 助教授 (00291477)

Co-Investigator(Kenkyū-buntansha) JIMBO Michio  Hiroshima Univ., Graduate school of Math., Prof., 大学院・数理科学研究科, 教授 (80109082)
TANISAKI Toshiyuki  Hiroshima Univ., Graduate school of Sci., Prof., 大学院・理学研究科, 教授 (70142916)
EGUCHI Masaaki  Hiroshima Univ., Fac. of Integrated Arts & Sci., Prof., 総合科学部, 教授 (30037220)
TAKEBE Takashi  Ochanomizu Univ., Dept. of Math., Assoc. Prof., 理学部, 助教授 (60240727)
Project Period (FY) 1999 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2001: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2000: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1999: ¥1,500,000 (Direct Cost: ¥1,500,000)
Keywordselliptic quantum group / solvable lattice model / affine Lie algebra / parafermion / quantum group / elliptic function / 量子群 / アフィン リー環 / アフィンリー環 / 可積分系 / 頂点作用素 / W-代数 / 共形場理論 / q-変形 / 散乱理論
Research Abstract

1. Formulation of the ABF model in regime II in terms of the vertex operators
Supposing the local height restriction is κ + 1, we have identified the half-infinite row and column transfer matrices and the creation operator of the physical excitation with the vertex operators and the basic q-parafermion currents of the q-deformed Ζ_κ parafermion theory, respectively. We have also shown that the scaling limit of the model is given by Koberle-Swieca's factorized scattering theory.
2. Representation of <sl>^^^^_2 in the principal gradation
We have given a free field realization of the representation of <sl>^^^^_2 in the generic level principal gradation. Especially, we have given a free field realization of Lepowsky-Wilson's Ζ-algebra as the deformed Virasoro algebra Vir_<q, t> in the limit (t = -q^<(k+22)/2>, q → 1).
3. Higher level representation of the elliptic quantum group β_<q,【lambda bar】>(<sl>^^^^_2)
Based on the free field realization of β_<q,【lambda bar】>(<sl>^^^^_2) and the elliptic algebra U_<q, p>(<sl>^^^^_2), we have given a systematic construction of the higher spin intertwining operators of β_<q,【lambda bar】>(<sl>^^^^_2). We have also clarified a relation between the coset decomposition of the tensor product of two U_q(<sl>^^^^_2)-modules and the representation of U_<q, p>(<sl>^^^^_2).

Report

(4 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • Research Products

    (31 results)

All Other

All Publications (31 results)

  • [Publications] Hitoshi Konno: "Fusion Construction of the Vertex Operators in Higher Level Reresentation of the Elliptic Quantum Group"Proceedings of APCTP-Nankai Symposium on Mathematical Physics, International J. of Modem Physics B. (出版予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Yuji Hara: "On Lepowsky-Wilson's Z-algebra"Proceedings of the workshop on Infinite-Dimensional Lie Theory and Conformal Field Theory. (出版予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Michio Jimbo: "Free Field Construction for the ABF Models in Regime II"Journal of Statistical Physics. 102. 883-921 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Yuji Hara: "Free Field Approach to the Dilute A_L Models"J. of Math. Phys.. 40. 3791-3826 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M.Eguchi: "An L^p Version of thg Hardy Theorem for Motion Groups"J. Austral. Math. Soc. Ser.. A68. 55-67 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M.Ebata: "A Generalization of the Hardy Theorem to Semisimple Lie Groups"Proc. Japan Acad. Ser. A Math. Sci.. 75. 113-114 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Tanisaki: "Hypergeometric Systems and Radon Transforms for Hermitian Symmetric spaces"Adv. Stud. Pure Math.. 26. 235-263 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M.Kashiwara: "Characters of Irreducible Modules with Non-critical Highest Weights over Affine Lie Algebras"China High. Educ. Press, Beijing. 275-296 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] B.Feigin: "Vertex Operator Algebras Arising from the Minimal Series M(3,p) and Monomial Basis"Proceedings of Math Phys Odyssey 2001-Integrable Models and Beyond, edited by M.Kashiwara and T.Miwa, Progress in Mathematics, Birkhauser. (出版予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] G.Kuroki: "Bosonization and Integral Representation of Solutions of the Knizhnik-Zamolodchikov-Bernard Equations"Commun. Math. Phys.. 204. 587-618 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Takebe: "A Note on Modified KP Hierarchy and Its (Yet Another) Dispersionless Limit"Letters in Mathematical Physics. (出版予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y. Hara, M. Jimbo, H. Konno, S. Odake and J. Shiraishi: "Free Field Approach to the Dilute A_L Moaeis"J of Math. Phys.. 40. 3791-3826 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M. Jimbo, H. Konno, S. Odake, Y. Pugai and J. Shiraishi: "Free Field Construction for the ABF Models in Regime II"J of Stat. Phys.. 102. 883-921 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Y. Hara, M. Jimbo, H. Konno, S. Odake and J. Shiraishi: "On Lepowsky-Wilson's Z-Algebra"Proceedings of the Conference on Infinite-Dimensional Lie Theory and Conformal Field Theory, edited by S. Berman et al, CONM series AMS., math. qa / 0005203. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] H. Konno: "Fusion Construction of the Vertex Operators in Higher Level Representation of the Elliptic Quantum Group"Proceedings of APCTP-Nankai Symposium on Mathematical Physics, edited by M.L.Ge and J.H.H.Perk, International Journal of Modern Physics B. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M. Eguchi, S. Koizumi, K. Kumahara: "An L Version of the Hardy Theorem for Motion Groups"J. Austral. Math. Soc. Ser.. A 68. 55-67 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M. Ebata, M. Eguchi, S. Koizumi, K. Kumahara: "A Generalization of the Hardy Theorem to Semisimple Lie Groups"Proc. Japan Acad. Ser. A Math, Sci.. 75. 113-114 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Tanisaki: "Hypergeometric Systems and Radon Transforms for Hermitian Symmetric spaces"Adv. Stud. Pure Math.. 26. MSJ, 235-263 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] B. Feigin, M. Jimbo and T. Miwa.: "Vertex Operator Algebras Arising from the Minimal Series M(3,p) and Monomial Basis"Proceedings of Math Phys Odyssey 2001- Integrable Models and Beyond, edited by M. kashiwara and T. Miwa, Progress in Mathematics, Birkhauser. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] G. Kuroki and T. Takebe: "Bosonization and Integral Representation of Solutions of the Knizhnik- Zamolodchikov-Bernard Equations"Commun. Math. Phys.. 204. 587-618 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Takebe: "A Note on Modified KP Hierarchy and Its (Yet Another) Dispersionless Limit"Letters in Mathematical Physics. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M. Kashiwara and T. Tanisaki: "Characters of Irreducible Modules with Non-critical Highest Weights over Affine Lie Algebras"China High. Educ. Press, Beijing. 275-296 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Hitoshi Konno: "Fusion Construction of the Vertex Operators in Higher Level Representation of the Elliptic Quantum Group"Proceedings of APCTP-Nankai Symposium on Mathematical Physics, International J. of Modern Physics B. (出版予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] Takashi Takebe: "A note on modified KP hierarchy and its(yet another)dispersionless limit"Letters in Mathematical Physics. (出版予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] B.Feigin: "Vertex operator algebras arising from the minimal series M(3, p)and monomial basis"Progress in Math.(MathPhys Odyssey 2001). (出版予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] Michio Jimbo: "On Lepowsky-Wilson's Z-algebra"Proceedings of the workshop on Infinite-Dimensional Lie Theory and Conformal Field Theory. (出版予定).

    • Related Report
      2000 Annual Research Report
  • [Publications] Toshiyuki Tanisaki: "Hypergeometric Systems and Radon Transforms for Hermitian Symmetric Spaces"Adv.Stud.Pure Math.. 26. 235-263 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Masaaki Eguchi: "An L^p Version of the Hardy Theorem for Motion Groups"J.Austral.Math.Sci.Ser.. A68. 55-67 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 神保道夫: "Free field construction for the ABF models in regime II"Journal of Statistical Physics. (出版予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] 谷崎俊之: "Hypergeometric systems and Radon transforms for Hermitian symmetric spaces"Adv.Stud.Pure Math. (出版予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] 江口正晃: "An Lspp version of the Hardy theorem for motion groups"J.Austral.Math.Soc.Ser.. A68. 55-67 (2000)

    • Related Report
      1999 Annual Research Report

URL: 

Published: 1999-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi