SkewHallLittlewoodPol: Skew Hall-Littlewood polynomial

In jack: Jack, Zonal, Schur, and Other Symmetric Polynomials

Skew Hall-Littlewood polynomial

Description

Returns the skew Hall-Littlewood polynomial associated to the given skew partition.

Usage

SkewHallLittlewoodPol(n, lambda, mu, which = "P")

Arguments

n	number of variables, a positive integer
lambda, mu	integer partitions defining the skew partition: lambda is the outer partition and mu is the inner partition (so mu must be a subpartition of lambda)
which	which skew Hall-Littlewood polynomial, "P" or "Q"

Value

A symbolicQspray multivariate polynomial, the skew Hall-Littlewood polynomial associated to the skew partition defined by lambda and mu. It has a single parameter usually denoted by t and its coefficients are polynomial in this parameter. When substituting t with 0 in the skew Hall-Littlewood P-polynomials, one obtains the skew Schur polynomials.

Examples

n <- 3; lambda <- c(3, 2, 1); mu <- c(1, 1)
skewHLpoly <- SkewHallLittlewoodPol(n, lambda, mu)
skewSchurPoly <- SkewSchurPol(n, lambda, mu)
substituteParameters(skewHLpoly, 0) == skewSchurPoly # should be TRUE

jack documentation built on Sept. 11, 2024, 6:34 p.m.