The vertex-algebras tag has no wiki summary.
1
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1answer
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Commutators of Schur polynomials of Lie algebra elements
Question:
Is there a well-known formula for computing the commutators of Schur polynomials when the variables are Lie algebra elements? If the algebra has a particularly simple commutation relation, ...
7
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0answers
160 views
Does the de Rham version of Cohen's theorem hold in the $\infty$-setting?
One of the first results that one needs to prove in the theory of chiral algebras is a de Rham version of Cohen's theorem on the homology of $C_n$ spaces. This is achieved in Beilinson-Drinfeld's book ...
7
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3answers
313 views
properties of formal delta functions
The formal delta function is
$\,\,\displaystyle\delta(x):=\sum_{n\in\mathbb Z}x^n.
$
If we agree that expressions $(x+y)^n$ for $n\in\mathbb Z$ are always expanded in non-negative powers of the second ...
4
votes
0answers
102 views
Arithmetic analogs of vertex algebras?
Has anyone successfully defined and studied analogs of vertex algebras where the grading of the fields is by $(\log \mathbb Q)$ rather than $\mathbb Z$? What I mean is that the usual fields
$$
a(z) = ...
3
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0answers
154 views
Does the following first order approximation of the Kapranov-Vasserot infinitesimal loops still do any job?
Let $X$ be a scheme over, say, a field $k$. Let us denote $\mathrm{Spec}(k[\varepsilon])$ by $T$ and its (unique) $k$-point by $0\in T$. Call the first order infinitesimal cone $C_{T,0}(X)$ over $X$ ...
11
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1answer
367 views
$\text{Rep}(D(G))$ as representation category of a vertex operator algebra
The category of representations $\text{Rep}(D(G))$ of the quantum double of a finite group is well-known to be a modular tensor category. Can these modular tensor categories also be obtained as ...
21
votes
5answers
1k views
Verlinde's formula
"Verlinde's formula" predicts the dimension of the space of conformal blocks of a chiral CFT.
Depending on...
• which chiral CFT one considers (does one restrict to WZW models, or not?)
...
3
votes
0answers
164 views
$\mathbb Z/2$-orbifolds in Virasoro representations, CFTs, VOAs
Suppose that ${\rm Vir}_c$ is a rational Virasoro algebra with central charge $c$.
Then ${\rm Vir}_c$ has finitely many irreducible modules $M_h$, parametrised by the highest weights $h$.
Furthermore ...
14
votes
2answers
583 views
Is this a vertex algebroid?… What is vertex algebroid?
A couple of day ago, I was lamenting to a friend about the fact that I have no idea what vertex algebroids are.
During our discussion, I came up with a guess of what a vertex algebroid might be.
I'm ...
15
votes
1answer
408 views
Character of parity-twisted supersymmetric VOA module — question inspired by the Stolz-Teichner program
I'll begin with some background that is unnecessary for the actual question, but that might be interesting to the reader:
Topological modular forms ($TMF$) is a generalized cohomology theory whose ...
13
votes
2answers
815 views
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 ...
11
votes
1answer
584 views
different N=2 SUSY structures on the chiral de Rham complex of a Calabi-Yau manifold?
The context
In a beautiful paper, Malikov-Schechtman-Vaintrob defined a canonical sheaf of vertex algebras equipped with a differential on any manifold $X$ (either in the $C^\infty$, complex analytic ...
32
votes
1answer
1k views
H^4 of the Monster
The Monster group $M$ acts on the moonshine vertex algebra $V^\natural$.
Because $V^\natural$ is a holomorphic vertex algebra (i.e., it has a unique irreducible module), there is a corresponding ...
10
votes
1answer
464 views
Is there a canonical map between the cohomology of orbifold Chiral de Rham on an orbifold and the cohomology of Chiral de Rham on a crepant resolution?
The two-variable elliptic genus is a topological invariant of almost-complex manifolds that takes values in power series. These power series turn out to describe weak Jacobi forms when the manifold ...
