Skip to main content

Lie algebras in Fock space

  • Chapter
Complex Analysis and Related Topics

Part of the book series: Operator Theory Advances and Applications ((OT,volume 114))

Abstract

A catalogue of explicit realizations of representations of Lie (super) algebras and quantum algebras in Fock space is presented.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Y. F. Smirnov and A. V. Turbiner, “Lie-algebraic discretization of differential equations”, Modern Physics Letters A10, 1795–1802 (1995), ERRATUM-ibid A10, 3139 (1995); “Hidden s12-algebra of finite-difference equations, Proceedings of IV Wigner Symposium, World Scientific, 1996, N.M. Atakishiyev, T.H. Seligman and K.B. Wolf (Eds.), pp. 435–440

    Google Scholar 

  2. A.M. Perelomov, “Generalized coherent states and its applications”, Nauka, 1987 (in Russian)

    Google Scholar 

  3. A. González-Lopéz, N. Kamran and P.J. Olver, “Quasi-Exactly-Solvable Lie Algebras of the first order differential operators in Two Complex Variables”, J. Phys. A24 (1991) 3995–4008; “Lie algebras of differential operators in two complex variables”, American J. Math. 114 (1992) 1163–1185

    Google Scholar 

  4. L. Brink, A. Turbiner and N. Wyllard, “Hidden Algebras of the (super) Calogero and Sutherland models,” J. Math. Phys. 39 (1998) 1285–1315. hep-th/9705219

    Article  MathSciNet  MATH  Google Scholar 

  5. M.A. Shifman and A.V. Turbiner, “Quantal problems with partial algebraization of the spectrum”, Comm. Math. Phys. 126 (1989) 347–365

    Article  MathSciNet  MATH  Google Scholar 

  6. O. Ogievetsky and A. Turbiner, “ sl(2, R) q and quasi-exactly-solvable problems”, Preprint CERN-TH: 6212/91 (1991) (unpublished)

    Google Scholar 

  7. A. V. Turbiner, “Lie algebras and linear operators with invariant subspace,” in Lie algebras, cohomologies and new findings in quantum mechanics (N. Kamran and P. J. Olver, eds.), AMS, vol. 160, pp. 263–310, 1994; “Lie-algebras and Quasi-exactly-solvable Differential Equations”, in CRC Handbook of Lie Group Analysis of Differential Equations, Vol.3: New Trends in Theoretical Developments and Computational Methods, Chapter 12, CRC Press (N. Ibragimov, ed.), pp. 331–366, 1995

    Google Scholar 

  8. C. Zachos, “Elementary paradigms of quantum algebras”, AMS Contemporary Mathematics, 134, 351–377; J. Stasheff and M. Gerstenhaber (eds.), AMS, 1991

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Basel AG

About this chapter

Cite this chapter

Turbiner, A. (2000). Lie algebras in Fock space. In: de Arellano, E.R., Vasilevski, N.L., Shapiro, M., Tovar, L.M. (eds) Complex Analysis and Related Topics. Operator Theory Advances and Applications, vol 114. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8698-7_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8698-7_18

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9734-1

  • Online ISBN: 978-3-0348-8698-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics