IJPAM: Volume 30, No. 4 (2006)

GENERALIZED BINOMIAL COEFFICIENTS ASSOCIATED
WITH COMPLEX ZONAL POLYNOMIALS

Francisco José Caro$^1$, Daya K. Nagar$^2$
$^{1,2}$Departamento de Matemáticas
Universidad de Antioquia
Calle 67, No. 53-108, Medellín, COLOMBIA
$^1$e-mail: fjcaro@matematicas.udea.edu.co
$^2$e-mail: nagar@matematicas.udea.edu.co


Abstract.The generalized binomial coefficient $\binom{\lambda}{\kappa}$ associated with complex zonal polynomials $\tilde{C}_{\kappa}(X)$ is defined as the coefficient of ${\tilde{C}_{\kappa}(X)}/{\tilde{C}_{\kappa}(I_{m})}$ in the complex binomial expansion

\begin{displaymath} \frac{\tilde{C}_{\lambda}(I_{m}+X)}{\tilde{C}_{\lambda}(I_{m... ...ppa}} \frac{\tilde{C}_{\kappa}(X)}{\tilde{C}_{\kappa}(I_{m})}. \end{displaymath}

In this article we have derived several results which facilitate computations of these coefficients.

Received: June 28, 2006

AMS Subject Classification: 62E15, 60E05

Key Words and Phrases: Hermitian matrix, generalized binomial coefficients, linear group, zonal polynomials

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 4