ZonalQR function

Evaluation of quaternionic zonal polynomials

Evaluates a quaternionic (or symplectic) zonal polynomial.

ZonalQR(x, lambda, algorithm = "DK")

Arguments

• x: numeric or complex vector or bigq vector
• lambda: an integer partition, given as a vector of decreasing integers
• algorithm: the algorithm used, either "DK" (Demmel-Koev) or "naive"

Returns

A numeric or complex scalar or a bigq rational number.

Examples

lambda <- c(2,2)
ZonalQR(c(3,1), lambda)
ZonalQR(c(gmp::as.bigq(3),gmp::as.bigq(1)), lambda)
##
x <- c(3,1)
ZonalQR(x, c(1,1)) + ZonalQR(x, 2) # sum(x)^2
ZonalQR(x, 3) + ZonalQR(x, c(2,1)) + ZonalQR(x, c(1,1,1)) # sum(x)^3

References

F. Li, Y. Xue. Zonal polynomials and hypergeometric functions of quaternion matrix argument. Comm. Statist. Theory Methods, 38 (8), 1184-1206, 2009

See Also

ZonalQPolR