# Invariant theory and the Heisenberg vertex algebra

Andrew R. Linshaw

Arxiv ID: 1006.5620•Last updated: 5/21/2021

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).

#### PaperStudio AI Chat

I'm your research assistant! Ask me anything about this paper.