An addition theorem for someq-Hahn polynomials


Theq-Hahn polynomials appear as functions on the lattice of subspaces of a finite-dimensional vector space over a finite field. Irreducible representations of the related general linear group are restricted to a maximal parabolic subgroup, and a specific description of the resulting irreducible components leads to an addition formula.

This is a preview of subscription content, access via your institution.


  1. [1]

    Andrews, G.: On the foundations of combinatorial theory V: Eulerian differential operators. Stud. Appl. Math.50, 345–375 (1971).

    Google Scholar 

  2. [2]

    Andrews, G.: Applications of basic hypergeometric functions. SIAM Rev.16, 441–484 (1974).

    Google Scholar 

  3. [3]

    Andrews, G., andR. Askey: The Classical Orthogonal Polynomials and their Discrete andq-Analogues. (To appear.)

  4. [4]

    Curtis, C., N. Iwahori, andR. Kilmoyer: Hecke algebras and characters of parabolic type of finite groups with (B, N)-pairs. I. H. E. S.40, 81–116 (1971).

    Google Scholar 

  5. [5]

    Delsarte, Ph.: Hahn Polynomials, Discrete Harmonics, andt-Designs. MBLE Report 295, April 1975.

  6. [6]

    Delsarte, Ph.: Bilinear Forms Over a Finite Field, With Applications to Coding Theory. MBLE Report R 327, April 1976.

  7. [7]

    Delsarte, Ph.: Association schemes andt-designs in regular semilattices. J. Comb. Th. A20, 230–243 (1976).

    Google Scholar 

  8. [8]

    Dunkl, Ch.: An addition theorem for Hahn polynomials: the spherical functions. SIAM J. Math. Anal.22 (1977).

  9. [9]

    Dunkl, Ch.: Spherical functions on compact groups and applications to special functions. Symp. Math. (To appear.)

  10. [10]

    Hahn, W.: Über Orthogonalpolynome, dieq-Differenzengleichungen genügen. Math. Nachr.2, 4–34 (1949).

    Google Scholar 

  11. [11]

    Karlin, S., andJ. McGregor: The Hahn polynomials, formulas and an application. Scripta Math.26, 33–46 (1961).

    Google Scholar 

  12. [12]

    Sears, D.: On the transformation theory of basic hypergeometric functions. Proc. London Math. Soc. (2)35, 158–180 (1951).

    Google Scholar 

  13. [13]

    Stanton, D.: A product-formula forq-Hahn polynomials. Notices Amer. Math. Soc.24, A-86 (1977).

    Google Scholar 

  14. [14]

    Steinberg, R.: A geometric approach to the representations of the full linear group over a Galois field. Trans. Amer. Math. Soc.71, 274–282 (1951).

    Google Scholar 

Download references

Author information



Additional information

During the preparation of this paper, the author was partially supported by NSF grant MCS76-07022.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Dunkl, C.F. An addition theorem for someq-Hahn polynomials. Monatshefte für Mathematik 85, 5–37 (1978).

Download citation


  • Vector Space
  • Irreducible Representation
  • General Linear
  • Irreducible Component
  • Finite Field