Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cosets of free field algebras via arc spaces   Using the invariant theory of arc spaces, we find minimal strong generating
sets for certain cosets of affine vertex algebras inside free field algebras
that are related to classical Howe duality. These results have several
applications. First, for any vertex algebra $\mathcal V$, we have a surjective
homomorphism of differential algebras $\mathbb{C}[J_{\infty}(X_{\mathcal V})]
\rightarrow \text{gr}^F(\mathcal V)$; equivalently, the singular support of
$\mathcal V$ is a closed subscheme of the arc space of the associated scheme
$X_{\mathcal V}$. We give many new examples of classically free vertex algebras
(i.e., this map is an isomorphism), including $L_k(\mathfrak{sp}_{2n})$ for all
positive integers $n$ and $k$. We also give new examples where the kernel of
this map is nontrivial but is finitely generated as a differential ideal. Next,
we prove a coset realization of the subregular ${\mathcal W}$-algebra of
$\mathfrak{sl}_n$ at critical level that was previously conjectured by
Creutzig, Gao, and the first author. Finally, we give some new level-rank
dualities involving affine vertex superalgebras.

29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int