Skip to main content
SpringerLink
Log in

Witten’s Approach, Braid Group Representations and X-Deformations

  • Conference paper
Nonlinear Physics

Part of the book series: Research Reports in Physics ((RESREPORTS))

  • 215 Accesses

Abstract

The Witten’s approach of link polynomials based on (2+1) Chern-Simons Lagrangian is used to simplify the calculations of braid group representations(BGR) for SU(2) algebra. On the basis of the direct derivations of BGR the “x-deformation” scheme is presented to generate explicitly the quantum R(x)-matrix for given BGR.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Birman J.S. Ann Math Studies No.82,(1976) Princeton University Press.

    Google Scholar 

  2. Birman J.S. and Wenzel, H. “Braids,Link Polynomials and a new algebra”,to appear in Trans A.M.S.

    Google Scholar 

  3. Frohlich,J. “Statistics of fields,the Yang-Baxter equatoins and the theory of Knots and links,ETH-Honggerberg preprint.

    Google Scholar 

  4. Jones, V.F.R. Bull Amer Math Soc.12,103(1985) Ann of Math 126,335(1987)

    Google Scholar 

  5. ).Jones, V.F.R, V.F.R. “On knot invariants related to some statistical mechanics models ”,jpreprint 1988.

    Google Scholar 

  6. Kauffman L.H. “State model for knot polynomials— An introduction”,preprint. Ann of Math Studies # 115.

    Google Scholar 

  7. Kauffman, L.H, L.H. “Knot theory and Applications”,talk at UT Austin,March 1988

    Google Scholar 

  8. Kauffman, L.H. “Braid Group,Knot Theory and Statistical Mechanics” P.27,edited C.N.Yang,World Scientific,1989.

    Google Scholar 

  9. Akutsu,Y. and Wadati, M. J.Phys soc Jan,56, 839, 3039 (1987)

    Article  MathSciNet  Google Scholar 

  10. Akutsu, Y. and Wadati, M. “Braid Group,Knot Theory and Statistical Mechanics”,p 151, edited by C.N.Yang,World Scientific,1989.

    Google Scholar 

  11. Turaev, V.G. Invent Math 92, 527 (1988)

    MathSciNet  Google Scholar 

  12. Reshetikhin, N. “Quantized universal enveloping algebras,the Yang-Baxter equation and invariants of links I,II” LOMT preprint E-4–87

    Google Scholar 

  13. kohno, T. “Quantum University enveloping algebras and monodromy of braid group” Nagoya preprint 1989

    Google Scholar 

  14. kohno, T. Nankai lectures on Math Physics,Tianjin,1988.

    Google Scholar 

  15. Takhtajan, L., Nankai lectures on Quantum Group,Tianjin,1989.

    Google Scholar 

  16. Witten, E. Comm Math Phys, 121, 135 (1989)

    MathSciNet  Google Scholar 

  17. Ge, M.L., Wang, L.Y., Xue, K., and Wu, Y.S., Inter J.Mod Phys 4, 3351 (1989).

    MathSciNet  Google Scholar 

  18. Lee, H.C., Ge, M.L.,Couture, M. and Wu, Y.S., Inter J.Mod Phys 4, 2333 (1989)

    MathSciNet  Google Scholar 

  19. Jimbo, M. Lett Math Phys 10, 63 (1985).

    MathSciNet  Google Scholar 

  20. Jimbo, M. Comm Math Phys 102, 537 (1986).

    MathSciNet  Google Scholar 

  21. Timbo, M., Lett Math Phys 11, 253 (1986)

    Google Scholar 

  22. Moore, G. and Seiberg, N., Phys Lett B212,451(1988),IAS preprint,HEP-88/39.

    Google Scholar 

  23. Kniznik, V G and Zamolodchikov, A.B. Nucl Phys B2147, 83 (1984).

    Article  ADS  Google Scholar 

  24. Ge, M.L., Wang L.Y. and Xue K, “Extended State Expandions and the University of Witten’ Version of Link Polynomial Theory” Nankai preprint 1989,to appear in Inter.Mod Phys.

    Google Scholar 

  25. Yamagishi, K., Ge M.L., and Wu Y.S., UU—HEP-89–1. “New Hierachies of Knot Polynomials from Topological Chern—Simons gauge Theory”.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theoretical Physics Division, Nankai Institute of Mathematics, Tianjin, 300071, People’s Rep. of China

    M. L. Ge, F. Piao, L. Y. Wang & K. Xue

Authors
  1. M. L. Ge
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Piao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. Y. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Science and Technology of China, 230026, Hefei, Anhui, People’s Rep. of China

    Chaohao Gu  & Yishen Li  & 

  2. Computing Center of Academia Sinica, 100080, Beijing, People’s Rep. of China

    Guizhang Tu

  3. Department of Mathematics, University of Science and Technology of China, 230026, Hefei, Anhui, People’s Rep. of China

    Yunbo Zeng

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin, Heidelberg

About this paper

Cite this paper

Ge, M.L., Piao, F., Wang, L.Y., Xue, K. (1990). Witten’s Approach, Braid Group Representations and X-Deformations. In: Gu, C., Li, Y., Tu, G., Zeng, Y. (eds) Nonlinear Physics. Research Reports in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84148-4_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-84148-4_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52389-5

  • Online ISBN: 978-3-642-84148-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation