The wonderful compactification for quantum groups Journal Article

Author(s): Ganev, Iordan
Article Title: The wonderful compactification for quantum groups
Affiliation IST Austria
Abstract: In this paper, we introduce a quantum version of the wonderful compactification of a group as a certain noncommutative projective scheme. Our approach stems from the fact that the wonderful compactification encodes the asymptotics of matrix coefficients, and from its realization as a GIT quotient of the Vinberg semigroup. In order to define the wonderful compactification for a quantum group, we adopt a generalized formalism of Proj categories in the spirit of Artin and Zhang. Key to our construction is a quantum version of the Vinberg semigroup, which we define as a q-deformation of a certain Rees algebra, compatible with a standard Poisson structure. Furthermore, we discuss quantum analogues of the stratification of the wonderful compactification by orbits for a certain group action, and provide explicit computations in the case of SL2.
Keywords: 16T99; 20G05; 20G42 (primary)
Journal Title: Journal of the London Mathematical Society
ISSN: 00246107
Publisher: John Wiley and Sons Ltd  
Date Published: 2018-11-22
Start Page: in press
Copyright Statement: CC BY 4.0
DOI: 10.1112/jlms.12193
Open access: yes (OA journal)