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Duflo--Serganova functor for chiral differential operators on classical invariant rings
Abstract
We study the Duflo--Serganova functor for vertex algebras of chiral differential operators on classical invariant rings, introduced in \cite{ADS}. Our main result is a general cancellation theorem showing that a common bosonic and fermionic summand can be removed by Duflo--Serganova reduction. We apply this theorem to obtain Duflo--Serganova reduction isomorphisms for two families of simple orthosymplectic affine vertex superalgebras at levels −2n and n, which are not covered by the existing results of Gorelik and Serganova. As a consequence, we obtain supercharacter identities, including the conjecture of Adamović and Milas as a special case.
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BibTeX
@misc{arakawa2026dufloserganova,
title = {{Duflo--Serganova functor for chiral differential operators on classical invariant rings}},
author = {Tomoyuki Arakawa and Xuanzhong Dai and Bailin Song},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34954},
eprint = {2610.34954},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34954},
}
RIS
TY - UNPB
TI - Duflo--Serganova functor for chiral differential operators on classical invariant rings
AU - Tomoyuki Arakawa
AU - Xuanzhong Dai
AU - Bailin Song
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34954
UR - https://arxiv.org/abs/2610.34954
AB - We study the Duflo--Serganova functor for vertex algebras of chiral differential operators on classical invariant rings, introduced in \cite{ADS}. Our main result is a general cancellation theorem showing that a common bosonic and fermionic summand can be removed by Duflo--Serganova reduction. We apply this theorem to obtain Duflo--Serganova reduction isomorphisms for two families of simple orthosymplectic affine vertex superalgebras at levels −2n and n, which are not covered by the existing results of Gorelik and Serganova. As a consequence, we obtain supercharacter identities, including the conjecture of Adamović and Milas as a special case.
ER -