Mapping class group representations from Drinfeld doubles of finite groups
2020 (English)In: Journal of knot theory and its ramifications, ISSN 0218-2165, Vol. 29, no 5, article id 2050033Article in journal (Refereed) Published
Abstract [en]
We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of such representations in terms of finite group data. This allows us to establish various properties of these representations. In particular we show that they have finite images, and that for surfaces of genus at least 3 their restriction to the Torelli group is non-trivial iff G is non-abelian.
Place, publisher, year, edition, pages
World Scientific Publishing Co. Pte Ltd , 2020. Vol. 29, no 5, article id 2050033
Keywords [en]
Quantum representation, mapping class group, Drinfeld double
National Category
Algebra and Logic Other Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-83725DOI: 10.1142/S0218216520500339ISI: 000546039600010Scopus ID: 2-s2.0-85085591170OAI: oai:DiVA.org:oru-83725DiVA, id: diva2:1448009
Funder
Swedish Research Council, 621-2013-4207 2017-03836
Note
Funding Agencies:
network " Interactions of Low-Dimensional Topology and Geometry with Mathematical Physics" (ITGP) of the European Science Foundation
VR Swedish Research Links Programme 348-2008-6049
Ministry of Education, China
Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)
China Science Postdoc Grant 2011M500887
2020-06-262020-06-262020-08-14Bibliographically approved