# Tag Info

Accepted

### q-Virasoro and q-Heisenberg algebras

The main sources are Awata et al or Frenkel-Reshetikhin. In http://arxiv.org/pdf/q-alg/9507034v5.pdf section 4, you can see the q,t case. You can also look at http://arxiv.org/pdf/q-alg/9505025v1.pdf ...
• 938
Accepted

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

Let $\mathfrak{g}$ be a complex Lie algebra with a distinguished nonzero central element $x$, and let $V$ be an irreducible representation of $\mathfrak{g}$. The usual proof of Schur's lemma can be ...
• 43.5k

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

For any group $G$ and subgroup $K$, there is an isomorphism $$H^*_G(G/K)= H^*_K(pt)$$ So the cohomology in question is $H^*_{S^1}(pt)=\mathbb Z[x]$, and it does not seem to be very related to the ...
• 41.2k

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

The terminology is explained earlier on that page and the previous page in the paper. On the same page, we see that they set $\mathfrak{g} = \mathfrak{su}(2) \times \mathfrak{su}(2)$, and let the ...
• 43.5k

### Poisson vertex algebra

This is an exercise problem and it is more proper to ask it on stack exchange. Your problem is that you do not know how to evaluate $Y_{-}(a\cdot b,z)$ for arbitrary $a,b$ in the Poisson vertex ...
• 31

### Two questions on Zuber's "KdV and W-flows"

As for $I_4$ and $I_j$ for all $j\geqslant 4$ up to overall sign factors, see e.g. equation (1.9) of these lecture notes with $u=-r$. Also you may wish to look at this link. Regarding the bracket at ...
• 5,123

### Link between Virasoro algebra and Heisenberg algebra

This construction comes out of string theory. You can find it described in your favorite string theory textbook. Green, Schwarz and Witten and Polchinski are standard references.
• 5,191