Miscellaneous functions
Functions related to Specht modules
dimension_specht_module
— Functiondimension_specht_module(mu::Partition{T}) where T <: IntegerUnion -> ZZRingElem
Return the dimension of the Specht module for mu
.
Examples
julia> print([dimension_specht_module(p) for p in partitions(4)])
ZZRingElem[1, 3, 2, 3, 1]
gram_determinant_specht_module
— Functiongram_determinant_specht_module(mu::Partition{T}) where T <: IntegerUnion
Return the determinant of the Gram matrix for the Specht module for mu
, in factorized collected form.
Examples
julia> print(gram_determinant_specht_module(partition([4, 3, 2, 1])))
Vector{ZZRingElem}[[3, 1152], [5, 768], [7, 384]]