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The center of small quantum groups II: singular blocks.
- Source :
-
Proceedings of the London Mathematical Society . Mar2019, Vol. 118 Issue 3, p513-544. 32p. - Publication Year :
- 2019
-
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 lth root of unity is formulated in type A. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00246115
- Volume :
- 118
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Proceedings of the London Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 135019052
- Full Text :
- https://doi.org/10.1112/plms.12193