User:Sylvain Ribault/sandbox

W-algebra

Null vectors of W3: reference or formulas?

Degenerate representations of W(N): paraphrase article on boundary Toda. Plenty of rep. theory of Lie algebra. Do it on paper first, replace alpha with P.

Correlation functions, fusion multiplicities, descendants not from primaries.

Differential equations, hypergeometric.

Add refs. Link to Toda. W minimal models.

Representation theory of semisimple Lie algebras

Weight (representation theory)

Theorem of the highest weight

Representation theory

Orthogonal group says nothing on representation theory save a link to Brauer algebra.

Linear group says very little on representation theory. Also, article is for general fields, not complex numbers. General linear group talks about the group, not its representations. The two articles are basically redundant and could probably be merged, but this would take some work. It is simpler to work from General linear group and ignore the other article.

Representation theory of SL2(R) has the merit of existing. So does Representation of a Lie group.

Blog post with two references.

What a mess!

Just create an article on representations of complex classical Lie groups? Need to clarify the difference $GL_{n}$ versus $SL_{n}$ etc. What about the unitary group? Subsume the article on Tensor representation? Maybe not, as that article makes sense over other fields.

Add Newell-Littlewood numbers to the article on Littlewood-Richardson coefficients. For finite group rank, blog post gives modification and references.

Dimensions of reps: even for O(n), there is an old factorized formula. What El Samra and King did was to find a formula that is manifestly a factorized polynomial in n.

Managing citations in Wikidata

Template:Cite_Q allows citing references that were created in Wikidata. This looks like a very good idea, provided it is indeed easy to create new references, and find existing references. Find out if this can be done from a DOI or an (arXiv) URL.

See my question there: Template_talk:Cite_Q#Easily_generate_the_needed_Wikidata_objects? An important minority of scientific articles are already in Wikidata. I am directed to the old SourceMD tool aka QuickStatements.

Example: 10.1103/PHYSREVD.98.105001 , cited in Conformal field theory. Managed to create the corresponding object d:Q104451562 using the above SourceMD tool. Need to be looged in QuickStatements. Test: Trying to input the same DOI again, the tool detects that the corresponding object already exists.

Various tests

${\begin{array}{c|l|r|}1&123.2&34sdf\\\hline 12343&2&12\\\hline \end{array}}$

<PGFTikZ> test image

<PGFTikZPreamble>

\usepackage{tikz} \usetikzlibrary{arrows} \usetikzlibrary{intersections} \usetikzlibrary{calc}

</PGFTikZPreamble> \begin{tikzpicture}[scale=.8,every node/.style={minimum size=1cm}] %

  \begin{scope}[
          yshift=-83,every node/.append style={
          yslant=0.5,xslant=-1},yslant=0.5,xslant=-1
          ]
      \draw[step=4mm, black] (0,0) grid (5,5); 
      \draw[black,thick] (0,0) rectangle (5,5);%borders
      \fill[green] (2.05,2.05) rectangle (2.35,2.35); % center pixel
      \fill[green] (1.65,2.05) rectangle (1.95,2.35); %left
      \fill[green] (2.45,2.05) rectangle (2.75,2.35); %right
      \fill[green] (2.05,2.45) rectangle (2.35,2.75); %top
      \fill[green] (2.05,1.95) rectangle (2.35,1.65); %bottom

  \end{scope}

% % draw annotations %

  \draw[-latex,thick,green](-3,-2)node[left]{1 patch}
      to[out=0,in=200] (-1,-.9);

\end{tikzpicture} </PGFTikZ>

A test text

Failed to parse (unknown function "\require"): {\displaystyle \require{xyjax} E = mc^2 }