论文标题
块分解通过几何萨克等价
Block decomposition via the geometric Satake equivalence
论文作者
论文摘要
我们提供了新的证明，以描述在一个积极特征$ \ ell $（最初是由于Donkin）的领域，通过在Langlands Dual Group的Satake类别中工作，并应用Riche和Williamson开发的smith-treumann理论。在表示理论方面，我们的方法使我们能够为在同一块中链接两个权重的最小链的长度绑定，并为$ \ ell $ th of Unity的量子组的块分解提供新的证明。
We give a new proof for the description of the blocks in the category of representations of a reductive algebraic group $\mathbf{G}$ over a field of positive characteristic $\ell$ (originally due to Donkin), by working in the Satake category of the Langlands dual group and applying Smith-Treumann theory as developed by Riche and Williamson. On the representation theoretic side, our methods enable us to give a bound for the length of a minimum chain linking two weights in the same block, and to give a new proof for the block decomposition of a quantum group at an $\ell$-th root of unity.
