Skip to main content
SpringerLink
Log in

Bispherical functions on the symmetric group associated with the hyperoctahedral subgroup

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

We consider an arbitrary irreducible representation of a symmetric group S4m that has a B2m-invariant and a B2m-antiinvariant vector, where B2m is a hyperoctahedral subgroup of S4m. The main result is an expression for a matrix element corresponding to these two vectors in terms of an irreducible character of the symmetric group Sm.

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. R. Howe, “Perspectives on invariant theory: Schur duality, multiplicity — free actions and beyond,” in:The Schur Lectures 1992, Israel Mathematical Conference Proceedings, Vol. 8 (1995), pp. 1–182.

    Google Scholar 

  2. I. G. Macdonald,Symmetric Functions and Hall Polynomials, 2nd ed., Oxford Univ. Press (1995).

  3. A. Okounkov and G. Olshanski, “Shifted Schur functions II. Binomial formula for characters of classical groups and applications,” to appear in A. A. Kirillov's Seminar on Representation Theory,Am. Math. Soc. Translations.

  4. J. R. Stembridge, “On Schur'sQ-functions and the primitive idempotents of a commutative Hecke algebra,”J. Algb. Combinatorics,1, 71–95 (1992).

    Article  Google Scholar 

Download references

Authors
  1. V. N. Ivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The author is deeply grateful to G. I. Olshansky for posing the problem and for constant interest in the work.

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 240, 1997, pp. 96–114.

Supported by the International Soros Educational Program, Grant 2093s.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ivanov, V.N. Bispherical functions on the symmetric group associated with the hyperoctahedral subgroup. J Math Sci 96, 3505–3516 (1999). https://doi.org/10.1007/BF02175829

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02175829

Keywords

Search

Navigation