jack (version 6.1.0)

SkewHallLittlewoodPol: Skew Hall-Littlewood polynomial

Description

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

Usage

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

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.

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"

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