On Integrality of SO(n)-Level 2 TQFTs
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The Ohio State University / OhioLINK
2018
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| Online Access: | http://rave.ohiolink.edu/etdc/view?acc_num=osu1525703476442228 |
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ndltd-OhioLink-oai-etd.ohiolink.edu-osu15257034764422282021-08-03T07:06:47Z On Integrality of SO(n)-Level 2 TQFTs Wang, Yilong Mathematics Modular Categories TQFT Integrality In this thesis, we study properties of the TQFT associated to the modular category SO(p)-level 2 for an odd prime p. We compute the associated representation of the central extension of the mapping class group of the surface of genus one with one boundary component specialized at a simple object a of SO(p)-level 2. Let ζ be a primitive p-th root of unity. We show that for each a, there exists a full-rank free lattice over the ring of integers Z[ζ, i] inside the genus 1 specialized space at a that is preserved by the extended mapping class group action. We also show that for each a, the image of the extended mapping class group representation is finite. Finally, we relate the representations to the Weil representation over finite fields. 2018-11-07 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1525703476442228 http://rave.ohiolink.edu/etdc/view?acc_num=osu1525703476442228 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
| collection |
NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
Mathematics Modular Categories TQFT Integrality |
| spellingShingle |
Mathematics Modular Categories TQFT Integrality Wang, Yilong On Integrality of SO(n)-Level 2 TQFTs |
| author |
Wang, Yilong |
| author_facet |
Wang, Yilong |
| author_sort |
Wang, Yilong |
| title |
On Integrality of SO(n)-Level 2 TQFTs |
| title_short |
On Integrality of SO(n)-Level 2 TQFTs |
| title_full |
On Integrality of SO(n)-Level 2 TQFTs |
| title_fullStr |
On Integrality of SO(n)-Level 2 TQFTs |
| title_full_unstemmed |
On Integrality of SO(n)-Level 2 TQFTs |
| title_sort |
on integrality of so(n)-level 2 tqfts |
| publisher |
The Ohio State University / OhioLINK |
| publishDate |
2018 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=osu1525703476442228 |
| work_keys_str_mv |
AT wangyilong onintegralityofsonlevel2tqfts |
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1719454038443950080 |