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NumericalRepresentationTheory.jl
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dlfivefifty committed Nov 28, 2022
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2 changes: 1 addition & 1 deletion Project.toml
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name = "RepresentationTheory"
name = "NumericalRepresentationTheory"
uuid = "6b7c1d51-ecee-4149-97a8-50646b514dce"
authors = ["Sheehan Olver <[email protected]>"]
version = "0.1.0"
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6 changes: 3 additions & 3 deletions README.md
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# RepresentationTheory.jl
# NumericalRepresentationTheory.jl
A Julia package for representation theory of the symmetric group




This package supports basic representation theory of the symmetric group. One can form irreducible representations (irreps) by specifying the corresponding permutation, combine representations via direct sum and Kronecker product, and also calculate the resulting irrep multipliciplities. For example, the following code calculates the Kronecker coefficients of two irreps of S₇, specified by the partitions `5+1+1` and `2+2+2+1`:
```julia
julia> using RepresentationTheory, Permutations, Plots
julia> using NumericalRepresentationTheory, Permutations, Plots

julia> R₁ = Representation(5,1,1);

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julia> plot(multiplicities(R)) # We can also plot
```
<img src=https://github.com/dlfivefifty/RepresentationTheory.jl/raw/master/images/mults.png width=500 height=400>
<img src=https://github.com/dlfivefifty/NumericalRepresentationTheory.jl/raw/master/images/mults.png width=500 height=400>

In addition, one can find an orthogonal transformation that reduces a representation to irreducibles:
```julia
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4 changes: 0 additions & 4 deletions REQUIRE

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module RepresentationTheory
module NumericalRepresentationTheory
using Base, LinearAlgebra, Permutations, RecipesBase, Plots, SparseArrays
import Base: getindex, size, setindex!, maximum, Int, length,
==, isless, copy, kron, hash, first, show, lastindex, |, Integer, BigInt
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4 changes: 2 additions & 2 deletions test/runtests.jl
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using RepresentationTheory, Test
import RepresentationTheory: gelfandbasis
using NumericalRepresentationTheory, LinearAlgebra, Test
import NumericalRepresentationTheory: gelfandbasis

@testset "Representations" begin
σ = Partition([3,3,2,1])
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Registration pull request created: JuliaRegistries/General/73013

After the above pull request is merged, it is recommended that a tag is created on this repository for the registered package version.

This will be done automatically if the Julia TagBot GitHub Action is installed, or can be done manually through the github interface, or via:

git tag -a v0.1.0 -m "<description of version>" 5cd8f76c6b5624597386ef5767add3168339eeb9
git push origin v0.1.0

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