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virasoro_symmetries [2021/09/15 17:51]
Brian McPeak 		virasoro_symmetries [2021/09/15 17:52] (current)
Brian McPeak
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 If a Verma module $\mathcal{V}_\Delta$ has null vectors, then we can construct a new highest-weight representation by quotienting it by the subrepresentation constructed from its null vectors. in other words, If a Verma module $\mathcal{V}_\Delta$ has null vectors, then we can construct a new highest-weight representation by quotienting it by the subrepresentation constructed from its null vectors. in other words,
  
-$$ \mathcal R = \frac{\mathcal{V}_\Delta}{U(\mathcal{V}^+) |\chi \rangle}+$$ \mathcal R = \frac{\mathcal{V}_\Delta}{U(\mathcal{V}^+) |\chi \rangle} \, . $$
  
-This forms a **degenerate representation**.  All representations fall into one of these two classes.  The subresentations of a Verma module are constructed from their null vectors.+This forms a **degenerate representation**.  All representations are either Verma modules or degenerate representations. The latter are important in the study of [[minimal models]]. 
  
  
Last modified: 2021/09/15 17:51
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