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3 votes
2 answers
615 views

On how to diagonalize a Casimir element

$\DeclareMathOperator\U{U}\DeclareMathOperator\SU{SU}\DeclareMathOperator\SO{SO}$I'm trying to read the physics paper Two Dimensional QCD as a String Theory. I'm struggling with my ignorance about ...
3 votes
1 answer
213 views

GKO (or coset) construction - all possible highest weights $h$

I am reading the famous paper "Unitary Representations of the Virasoro and Super-Virasoro Algebras" by Goddard, Kent, Olive. From a compact simple Lie algebra $\mathfrak{g}$ and a Lie subalgebra $\...
1 vote
0 answers
80 views

GKO construction for (Super-)Virasoro algebras

I am reading the paper "Unitary Representations of the Virasoro and Super-Virasoro Algebras" by Goddard, Kent, Olive. In many places, the authors claim results without any justification, or with ...
3 votes
0 answers
150 views

Physical relevance of either fundamental identity generalizing Jacobi [closed]

There are two fundamental identities for n-ary generalizations of the Jacobi identity. One fundamental identity is right for Nambu mechanics and such, the other for L_\infty algebras as in CSFT. Which ...
5 votes
2 answers
847 views

CFTs corresponding to affine Lie algebras

I want to know how one can write down a CFT such that its conserved currents will satisfy some chosen (affine) Lie algebra $G$. On the few pages leading up to page 192 in here one can see see the ...