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arXiv · 1006.5620

Invariant theory and the Heisenberg vertex algebra

Andrew R. Linshaw
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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).

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Andrew R. Linshaw. 2011-09-05. Invariant theory and the Heisenberg vertex algebra. https://doi.org/10.1093/imrn%2Frnr171

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