The center of small quantum groups II: singular blocks
- Creators
- Lachowska, Anna
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Qi, You
Abstract
We generalize to the case of singular blocks the result in Bezrukavnikov and Lachowska [Quantum groups, Contemporary Mathematics 433 (American Mathematical Society, Providence, RI, 2007) 89–101] that describes the center of the principal block of a small quantum group in terms of sheaf cohomology over the Springer resolution. Then using the method developed in Lachowska and Qi [Int. Math. Res. Not., Preprint, 2017, arXiv:1604.07380], we present a linear algebro‐geometric approach to compute the dimensions of the singular blocks and of the entire center of the small quantum group associated with a complex semisimple Lie algebra. A conjectural formula for the dimension of the center of the small quantum group at an l th root of unity is formulated in type A.
Additional Information
© 2018 London Mathematical Society. Issue Online: 01 March 2019; Version of Record online: 13 September 2018; Manuscript revised: 06 July 2018; Manuscript received: 04 December 2017. The second named author is partially funded by the National Science Foundation, DMS-1763328. The authors would like to thank Sergey Arkhipov, Roman Bezrukavni‐kov, Peng Shan, Chenyang Xu and Zhiwei Yun for many helpful discussions. Special thanks are due to Igor Frenkel for suggesting an inspiring formula for the dimension of the center for small quantum groups in type A, and to Bryan Ford for his valuable help with coding the computations in type A3.Attached Files
Submitted - 1703.02457.pdf
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Additional details
- Eprint ID
- 97739
- Resolver ID
- CaltechAUTHORS:20190809-161407488
- DMS-1763328
- NSF
- Created
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2019-08-09Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field