Monatshefte für Mathematik

, Volume 85, Issue 1, pp 5–37 | Cite as

An addition theorem for someq-Hahn polynomials

  • Charles F. Dunkl


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.


Vector Space Irreducible Representation General Linear Irreducible Component Finite Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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.)Google Scholar
  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.Google Scholar
  6. [6]
    Delsarte, Ph.: Bilinear Forms Over a Finite Field, With Applications to Coding Theory. MBLE Report R 327, April 1976.Google Scholar
  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).Google Scholar
  9. [9]
    Dunkl, Ch.: Spherical functions on compact groups and applications to special functions. Symp. Math. (To appear.)Google Scholar
  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

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Charles F. Dunkl
    • 1
  1. 1.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

Personalised recommendations