Skip to main content
Log in

On the Multiplicity-Free Plethysms p 2[\({s_\lambda}\)]

  • Published:
Annals of Combinatorics Aims and scope Submit manuscript

Abstract

We determine all the shapes \({\lambda}\) such that the plethysms \({p_2}\)[\({s_\lambda}\)](x) of the power symmetric function \({p_2}\)(x) and the Schur function \({s_\lambda}\)(x) are multiplicity-free.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Carini L., Remmel J.B.: Formulas for the expansion of the plethysms \({s_{(2)}[s_{(a,b)}]}\) and \({s_{(2)}[s_{(n^k)}]}\). Discrete Math. 193(1-3), 147–177 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Carré C., Leclerc B.: Splitting the square of a Schur function into its symmetric and antisymmetric parts. J. Algebraic Combin. 4(3), 201–231 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen, Y.M., Garsia, A.M., Remmel, J.B.: Algorithms for plethysm. In: Greene, C. (ed.) Combinatorics and Algebra (Boulder, Colo., 1983), Contemp. Math., Vol. 34, pp. 109–153. Amer. Math. Soc., Providence, RI (1984)

  4. James, G.D., Kerber, A.: The Representation Theory of the Symmetric Group. Addison-Wesley, Reading, MA (1981)

  5. Littlewood D.E.: Invariant theory, tensors, and group characters. Philos. Trans. Roy. Soc. London Ser. A 239, 305–355 (1944)

    Article  MathSciNet  MATH  Google Scholar 

  6. Littlewood D.E.: Modular representations of symmetric groups. Proc. Roy. Soc. London Ser. A 209, 333–353 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  7. Littlewood D.E.: The Theory of Group Characters. 2nd edition. Oxford University Press, Oxford (1950)

    MATH  Google Scholar 

  8. Macdonald I.G.: Symmetric Functions and Hall Polynomials. Second edition. Oxford University Press, New York (1995)

    MATH  Google Scholar 

  9. Remmel J.B., Whitney R.: Multiplying Schur functions. J. Algorithms 5(4), 471–487 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  10. Sundquist, T.S.: Pfaffians, involutions, and Schur functions. Ph.D. Thesis, University of Minnesota, Minnesota (1992)

  11. Mizukawa H., Yamada H.-F.: Rectangular Schur functions and the basic representation of affine Lie algebras. Discrete Math. 298(1-3), 285–300 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Garoufalidis S., Morton H., Vuong T.: The SL3 colored Jones polynomial of the trefoil. Proc. Amer. Math. Soc. 141(6), 2209–2220 (2013)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Luisa Carini.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Carini, L. On the Multiplicity-Free Plethysms p 2[\({s_\lambda}\)]. Ann. Comb. 21, 339–352 (2017). https://doi.org/10.1007/s00026-017-0354-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00026-017-0354-0

Mathematics Subject Classification

Keywords

Navigation