Year: 2021
Type: article
Abstract: We give a complete classification of Airy structures for finite-dimensional simple Lie algebras over $${\mathbb {C}}$$ C , and to some extent also over $${\mathbb {R}}$$ R , up to isomorphisms and gauge transformations. The result is that the only algebras of this type which admit any Airy structures are $$\mathfrak {sl}_2$$ sl2 , $$\mathfrak {sp}_4$$ sp4 and $$\mathfrak {sp}_{10}$$ sp10 . Among these, each admits exactly two non-equivalent Airy structures. Our methods apply directly also to semisimple Lie algebras. In this case it turns out that the number of non-equivalent Airy structures is countably infinite. We have derived a number of interesting properties of these Airy structures and constructed many examples. Techniques used to derive our results may be described, broadly speaking, as an application of representation theory in semiclassical analysis.
Authors: Leszek Hadasz, Błażej Ruba
Institution: Jagiellonian University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,690
OpenAlex ID: W2991196355