Journal article
Comparing skein and quantum group representations and their application to asymptotic faithfulness
Pure and applied mathematics quarterly, Vol.12(4), pp.473-492
01/01/2016
DOI: 10.4310/PAMQ.2016.v12.n4.a2
Abstract
We make two related observations in this paper. First, the representations of mapping class groups from the Ising TQFT and its quantum group counterpart SU(2)(2) are neither equivalent as representations nor Galois conjugate to each other. Hence mapping class group representations obtained from quantum skein theory are fundamentally distinct from those obtained from quantum group Reshetikhin-Turaev or geometric quantization constructions. Then we generalize the asymptotic faithfulness of the skein quantum SU(2) representations of mapping class groups of orientable closed surfaces to skein quantum SU(3). We conjecture asymptotic faithfulness holds for skein quantum G representations when G is a simply-connected simple Lie group. The difficulty for such a generalization lies in the lack of an explicit description of the fusion spaces with multiplicities to define an appropriate complexity of state vectors.
Details
- Title: Subtitle
- Comparing skein and quantum group representations and their application to asymptotic faithfulness
- Creators
- Wade Bloomquist - University of California, Santa BarbaraZhenghan Wang - Microsoft
- Resource Type
- Journal article
- Publication Details
- Pure and applied mathematics quarterly, Vol.12(4), pp.473-492
- DOI
- 10.4310/PAMQ.2016.v12.n4.a2
- ISSN
- 1558-8599
- eISSN
- 1558-8602
- Publisher
- Int Press Boston, Inc
- Number of pages
- 20
- Grant note
- DMS-1410144; DMS-1411212 / NSF; National Science Foundation (NSF)
- Language
- English
- Date published
- 01/01/2016
- Academic Unit
- Mathematics
- Record Identifier
- 9984936617302771
Metrics
1 Record Views