Skip to main content
SpringerLink
Log in

Tensor Powers of the Defining Representation of \(S_n\)

  • Published:
Journal of Theoretical Probability Aims and scope Submit manuscript

Abstract

We give a decomposition formula for tensor powers of the defining representation of \(S_n\) and apply it to bound the mixing time of a Markov chain on \(S_n\).

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1965)

    MATH  Google Scholar 

  2. Diaconis, P.: Group Representations in Probability and Statistics, IMS Lecture Notes Monograph Series, vol. 11. Inst. Math. Statist, Hayward (1988)

    Google Scholar 

  3. Diaconis, P., Shahshahani, M.: Generating a random permutation with random transpositions. Z. Wahrsch. verw. Geb. 57(2), 159–179 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ding, S.: A random walk in representations. Ph.D. Thesis, University of Pennsylvania (2014)

  5. Frobenius, F.G.: Über die Charaktere der symmetrischen Gruppe. Sitz. Konig. Preuss. Akad. Wissen., 516–534 (1900) Reprinted in: Frobenius, F.G.: Gesammelte Abhandlungen, vol. III (Serre, J.-P., ed.), 148–166. Springer, Berlin (1968)

  6. Fulman, J.: Separation cutoffs for random walk on irreducible representations. Ann. Comb. 14(3), 319–337 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fulton, W., Harris, J.: Representation Theory: A First Course, GTM 129. Springer, New York (1991)

    MATH  Google Scholar 

  8. Goupil, A., Chauve, C.: Combinatorial operators for Kronecker powers of representations of \(S_n\). Séminaire Lotharingien de Combinatoire 54, B54j (2006)

    MathSciNet  MATH  Google Scholar 

  9. James, G.D.: The Representation Theory of the Symmetric Groups, LNM 682. Springer, Berlin (1978)

    Book  Google Scholar 

  10. Saloff-Coste, L., Zúñiga, J.: Refined estimates for some basic random walks on the symmetric and alternating groups. ALEA Lat. Am. J. Probab. Math. Stat. 4, 359–392 (2008)

    MathSciNet  MATH  Google Scholar 

  11. Stanley, R.P.: Enumerative Combinatorics, vol. I. Wadsworth, Monterey (1986), Cambridge Stud. Adv. Math. 49, reprinted by Cambridge Univ. Press, Cambridge (1997)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 19104, USA

    Shanshan Ding

Authors
  1. Shanshan Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shanshan Ding.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ding, S. Tensor Powers of the Defining Representation of \(S_n\) . J Theor Probab 30, 1191–1199 (2017). https://doi.org/10.1007/s10959-016-0673-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10959-016-0673-9

Keywords

Mathematics Subject Classification (2010)

Search

Navigation