The center of small quantum groups II: singular blocks: THE CENTER OF SMALL QUANTUM GROUPS II: SINGULAR BLOCKS
The center of small quantum groups II: singular blocks: THE CENTER OF SMALL QUANTUM GROUPS II: SINGULAR BLOCKS
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小量子群的中心 II：奇异块： 小量子群的中心 II：奇异块
DOI：
10.1112/plms.12193
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发表时间：
2018
影响因子：
1.8
通讯作者：
Qi, You
中科院分区：
文献类型：
--
作者：
Lachowska, Anna;Qi, You
我们将Bezrukavnikov和Lachowska [Quantum groups，Contemporary Mathematics 433（American Mathematical Society，普罗维登斯，RI，2007）89-101]中的结果推广到奇异块的情况，该结果描述了在Springer分解上的层上同调的小量子群的主块的中心。然后使用Lachowska和Qi [Int. Math. Res. Not.，预印本，2017，arXiv：1604.07380]，我们提出了一种线性代数几何方法来计算与复半单李代数相关的小量子群的奇异块和整个中心的维数。给出了A型小量子群在单位根处的中心维数的一个解析公式。
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 anth root of unity is formulated in type A.