Graded super duality for general linear Lie superalgebras
Christopher Leonard
TL;DR
This paper proves a new form of super duality for infinite-rank general linear Lie superalgebras, establishing graded equivalences and Koszul properties in their BGG categories.
Contribution
It introduces a new proof of super duality using a uniqueness theorem for tensor product categorifications, and shows these categories have Koszul graded lifts.
Findings
Super duality equivalence between categories is established.
Categories admit Koszul graded lifts.
Super duality can be extended to a graded equivalence.
Abstract
We provide a new proof of the super duality equivalence between infinite-rank parabolic BGG categories of general linear Lie (super) algebras conjectured by Cheng and Wang and first proved by Cheng and Lam. We do this by establishing a new uniqueness theorem for tensor product categorifications motivated by work of Brundan, Losev, and Webster. Moreover we show that these BGG categories have Koszul graded lifts and super duality can be lifted to a graded equivalence.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.