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2 votes
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Monoidal category of irreducible highest weight modules of the Virasoro algebra

I'm trying to see if I can construct a monoidal category $\mathbf{C}$ whose objects are the irreducible unitary highest weight representations of the Virasoro algebra. I am thinking on doing the fol …
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7 votes
1 answer
1k views

The use of Schur's lemma for Lie algebras in physics (CFT)

Anytime a one-dimensional central extension appears in the physics literature, immediately they assume that in any irreducible representation the central charge will be a multiple of the identity, imp …
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3 votes
1 answer
207 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 $\ma …
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