Equivariant motivic Hall algebras
Algebraic Geometry
2018-09-10 v2 Category Theory
Representation Theory
Abstract
We introduce a generalization of Joyce's motivic Hall algebra by combining it with Green's parabolic induction product, as well as a non-archimedean variant of it. In the construction, we follow Dyckerhoff-Kapranov's formalism of 2-Segal objects and their transferred algebra structures. Our main result is the existence of an integration map under any suitable transfer theory, of course including the (analytic) equivariant motivic one. This allows us to study Harder-Narasimhan recursion formulas in new cases.
Keywords
Cite
@article{arxiv.1808.04165,
title = {Equivariant motivic Hall algebras},
author = {Thomas Poguntke},
journal= {arXiv preprint arXiv:1808.04165},
year = {2018}
}
Comments
37 pages; v2: several improvements throughout, added sketch proof to last section; comments welcome!