Equivariant motivic Hall algebras
Abstract
We introduce a generalization of Joyce's motivic Hall algebra by combining it with Green's parabolic induction product, as well as a nonarchimedean variant of it. In the construction, we follow DyckerhoffKapranov's formalism of 2Segal 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 HarderNarasimhan recursion formulas in new cases.
 Publication:

arXiv eprints
 Pub Date:
 August 2018
 arXiv:
 arXiv:1808.04165
 Bibcode:
 2018arXiv180804165P
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Category Theory;
 Mathematics  Representation Theory;
 14D10;
 14D20;
 14D23;
 16T10;
 18D10;
 18E10;
 18F30;
 18G30
 EPrint:
 37 pages