An update on Heisenberg and Kac-Moody categorification

Fuente: arXiv
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Main Authors: Brundan, Jonathan, Savage, Alistair, Webster, Ben
Format: Preprint
Published: 2025
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author Brundan, Jonathan
Savage, Alistair
Webster, Ben
author_facet Brundan, Jonathan
Savage, Alistair
Webster, Ben
contents Heisenberg categories act on many Abelian categories appearing in type A representation theory. There is also a general procedure to construct from a Heisenberg action another action of a Kac-Moody 2-category for some associated Cartan matrix. One of the adjunctions on the Kac-Moody side is matched up in an easy way with adjunctions on the Heisenberg side, but the second adjunction is much harder to describe. In this paper, we derive explicit formulae for this difficult adjunction, leading to some further simplifications to the existing theory.
format Preprint
id arxiv_https___arxiv_org_abs_2508_14378
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle An update on Heisenberg and Kac-Moody categorification
Brundan, Jonathan
Savage, Alistair
Webster, Ben
Representation Theory
17B37, 18M05, 18M30
Heisenberg categories act on many Abelian categories appearing in type A representation theory. There is also a general procedure to construct from a Heisenberg action another action of a Kac-Moody 2-category for some associated Cartan matrix. One of the adjunctions on the Kac-Moody side is matched up in an easy way with adjunctions on the Heisenberg side, but the second adjunction is much harder to describe. In this paper, we derive explicit formulae for this difficult adjunction, leading to some further simplifications to the existing theory.
title An update on Heisenberg and Kac-Moody categorification
topic Representation Theory
17B37, 18M05, 18M30
url https://arxiv.org/abs/2508.14378