Invariant theory and the Heisenberg vertex algebra

Abstract

The invariant subalgebra H^+ of the Heisenberg vertex algebra H under its automorphism group Z/2Z was shown by Dong-Nagatomo to be a W-algebra of type W(2,4). Similarly, the rank n Heisenberg vertex algebra H(n) has the orthogonal group O(n) as its automorphism group, and we conjecture that H(n)^{O(n)} is a W-algebra of type W(2,4,6,...,n^2+3n). We prove our conjecture for n=2 and n=3, and we show that this conjecture implies that H(n)^G is strongly finitely generated for any reductive group G\subset O(n).

Minor corrections, final version

References in corpus (3)

• Field Algebras
• Invariant subalgebras of affine vertex algebras
• A Hilbert theorem for vertex algebras

Cited by in corpus (15)

• Schur-Weyl Duality for Heisenberg Cosets
• Cosets of affine vertex algebras inside larger structures
• Simple current extensions beyond semi-simplicity
• Trialities of $\mathcal{W}$-algebras
• Orbifolds and cosets of minimal $\mathcal{W}$-algebras
• Trialities of orthosymplectic $\mathcal{W}$-algebras
• Invariant subalgebras of affine vertex algebras
• Cosets of the ${\mathcal{W}}^k({\mathfrak{sl}}_4,f_{\text{subreg}})$-algebra
• $N=4$ superconformal algebras and diagonal cosets
• Permutation Orbifolds of the Heisenberg Vertex Algebra $\mathcal{H}(3)$
• Generalized parafermions of orthogonal type
• On irreducibility of modules of Whittaker type for cyclic orbifold vertex algebra
• Vertex Algebras and Commutative Algebras
• Twisted representations of vertex operator algebras associated to affine Lie algebras
• The Z_2 Orbifold of the Universal Affine Vertex Algebra