Orbifolds of symplectic fermion algebras - Creutzig, Thomas; Linshaw, Andrew R. (Transactions of the American Mathematical Society, 2017)
We present a systematic study of the orbifolds of the rank n symplectic fermion algebra A(n), which has full automorphism group Sp(2n). First, we show that A(n)Sp(2n) and A(n)GL(n) are W-algebras of type W(2, 4,…, 2n) and W(2, 3,…, 2n + 1), respectively. Using these results, we find minimal strong finite generating sets for A(mn)Sp(2n) and A(mn)GL(n) for all m, n ≥ 1. We compute the characters of the irreducible representations of A(mn)Sp(2n)ï¿½SO(m) and A(mn)GL(n)ï¿½GL(m) appearing inside A(mn), and we express these characters using partial theta functions. Finally, we give a complete solution to the Hilbert problem for A(n); we show that for any reductive group G of automorphisms, A(n)G is strongly finitely generated.
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