# Questions tagged [virasoro-algebra]

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### Equivariant cohomology of $\text{Diff}S^1/ S^1$ and Virasoro

Consider $$\mathcal{M}\ =\ \text{Diff}S^1/S^1$$ which is a contractible complex manifold with an action of $\text{Diff}S^1$ by translations. It is claimed in page 358 of  that $\mathcal{M}$ has ...
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### Different views on Highest weight irreducible modules of the Virasoro algebra

Every highest weight irreducible representation of the Virasoro algebra can be labelled uniquely by a pair $(c,h)$ of complex numbers . This module can be written as quotient of the unique (up to ...
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### 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, ...
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### Link between Virasoro algebra and Heisenberg algebra

I'm reading these notes on infinite-dimensional Lie algebras. On page 5, author defines Heisenberg algebra and shows that certain infinite sums of elements of Heisenberg algebra (I'm being a little ...
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### Representations of infinite dimensional Lie algebras as vector fields on manifolds

Suppose I have e.g. the Witt algebra, $\left[l_n,l_m \right] = -(n-m)l_{n+m}$. I want to realize the $l_n$ as vector fields on some manifold. The classical example is when the $l_n$ span the Lie ...
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### I'm looking for a Virasoro-module whose character is 1+ 240q+ 2160q^2+ 6720q^3…

Let $E_4(q)=1+ 240q+ 2160q^2+ 6720q^3+\ldots$ be the Eisenstein series of weight 4, also known as the theta-series of the $E_8$-lattice. I'm looking for a $\mathbb N$-graded vector space $V$ of ...
For those who aren't familiar with the Virasoro or Temperley-Lieb algebras, I include some definitions: • The (universal envelopping algebra of the) Virasoro algebra is the $\star$-algebra \$...