Dimensions of irreducible representations of SU(n)

Version 1.0
Robert Coquereaux
CPT, CNRS, Luminy, Marseille

What the program does

Given an irreducible representation of SU(n) specified by the components of its highest weight in the basis of fundamental weights, the program determines its dimension.

Note: this is a very simple (and short) program. It was written mostly to test the Manipulate command and the code for the cdf file.
More interesting programs (product decomposition, multiplicities, intertwiners, pictographs, etc.) can be found by selecting one of the links, below.

Links

Related programs:

Notebooks (nb files, they also include the source code for the cdf version) 
(HyperlinkURL["Tensor product of SU(n) irreducible representations (Littlewood-Richardson coefficients)", http://www.cpt.univ-mrs.fr/~coque/Computer_programs/nb/tensorProdIrrep.nb])
(HyperlinkURL["Pictographs: oblades for SU(n)", http://www.cpt.univ-mrs.fr/~coque/Computer_programs/nb/obladesSUn.nb])
(HyperlinkURL["Pictographs: honeycombs for SU(n)", http://www.cpt.univ-mrs.fr/~coque/Computer_programs/nb/honeycombsSUn.nb])
(HyperlinkURL["Dimensions of irreps of SU(n)", http://www.cpt.univ-mrs.fr/~coque/Computer_programs/nb/dimensionsOfIrrepsSUn.nb])

CDF files (standalone)
for the Wolfram CDF Player
(HyperlinkURL["Tensor product of SU(n) irreducible representations (Littlewood-Richardson coefficients). CDF file", http://www.cpt.univ-mrs.fr/~coque/Computer_programs/cdf/tensorProdIrrep.cdf])
(HyperlinkURL["Pictographs: oblades for SU(n). CDF file", http://www.cpt.univ-mrs.fr/~coque/Computer_programs/cdf/obladesSUn.cdf])
(HyperlinkURL["Pictographs: honeycombs for SU(n). CDF file", http://www.cpt.univ-mrs.fr/~coque/Computer_programs/cdf/honeycombsSUn.cdf])
(HyperlinkURL["Dimensions of irreps of SU(n). CDF file", http://www.cpt.univ-mrs.fr/~coque/Computer_programs/cdf/dimensionsOfIrrepsSUn.cdf])

CDF files adapted to the first version of the CDF Player on IOS 
(when the latter is updated,  one should use the previous files instead):
(HyperlinkURL["Pictographs: oblades for SU(n). CDF file, IOS.", http://www.cpt.univ-mrs.fr/~coque/Computer_programs/cdf/obladesSUnForIOS.cdf])
(HyperlinkURL["Pictographs: honeycombs for SU(n). CDF file, IOS.", http://www.cpt.univ-mrs.fr/~coque/Computer_programs/cdf/honeycombsSUnForIOS.cdf])

Files for the cdf web plug-in 
(dying technology: the plug-in is incompatible with most recent browsers, these files will not be updated):
(HyperlinkURL["Tensor product of SU(n) irreducible representations (Littlewood-Richardson coefficients). CDF file for web plug-in", http://www.cpt.univ-mrs.fr/~coque/Computer_programs/cdf/tensorProdIrrepWeb.cdf])
(HyperlinkURL["Pictographs: oblades for SU(n). CDF file for web plug-in", http://www.cpt.univ-mrs.fr/~coque/Computer_programs/cdf/obladesSUnWeb.cdf])
(HyperlinkURL["Pictographs: honeycombs for SU(n). CDF file for web plug-in", http://www.cpt.univ-mrs.fr/~coque/Computer_programs/cdf/honeycombsSUnWeb.cdf])

DIMENSION OF AN IRREDUCIBLE REPRESENTATION OF SU(n)  -  Code -

dimensionIrrepSU[ruplet_]:=
With[{rk=Length[ruplet]},Product[With[{p=pval},Product[(p+Sum[ruplet[[t]],{t,s,s+p-1}]),{s,1,rk-(p-1)}]],{pval,1,rk}]/Product[x!, {x,1,rk}]]

DIMENSION OF AN IRREDUCIBLE REPRESENTATION OF SU(n)  -  Code for CDF Interface

With[{fieldSize=3,n=4},DynamicModule[{rows=1,cols=n-1,mat=Table[RandomInteger[3],{1},{n-1}],myRange},
myRange[s_]:= Range[s];
Dynamic@Manipulate[
Row[{"Dimension of",MatrixForm[mat]," = ",dimensionIrrepSU[First@mat]}],Evaluate@With[{makeRow=Function[{rowIndex}, Map[Function[{colIndex},InputField[Dynamic[mat[[rowIndex,colIndex]]],Number,FieldSize->fieldSize]],myRange[cols]],HoldAll]},
Row[{Grid[Map[makeRow,myRange[rows]]],Invisible["xxxxxx"],Column[{"Dimension of an irreducible representations specified by its higest weight.","Entries refer to the n-1 components of the chosen highest weights in the basis of fundamental weights (Dynkin basis).", Style["Use TAB or RETURN to update.",Brown],
Style["On IOS, use the Update button.",Brown]}]}]],
Row[{
Column[{Panel[Style[cols+1,FontSize->14,Bold],Style["SU(n), with n =",Bold, FontSize->12],Left,BaselinePosition->Bottom],
Button[Style["Update", Bold, FontSize->12,Blue],rows++;rows--;]}],
Panel[Style[Column[{"Dimension of an irreducible","representation of SU(n)"},Center], "Title"]]},Invisible["xxxxxx"]],
Button["Decrease n",
mat=Map[(Drop[#,-1])&,mat];
cols--;],
Button["Increase n",
AppendTo[mat[[1]],0];;
cols++;]],
SaveDefinitions->True,SynchronousUpdating-> False]]