论文标题
对称组的双重盖子和颤抖的Hecke Superalgebras的岩石块
RoCK blocks for double covers of symmetric groups and quiver Hecke superalgebras
论文作者
论文摘要
我们为对称组的双层覆盖定义和研究岩石块。我们证明，双层盖的岩石块与标准的“本地”块相当。对称组块的类似结果，即Chuang和Kessar的定理，是Chuang和Rouquier的重要一步，最终证明了Broué的Abelian Abelian缺陷组对对称组的猜想。确实，我们证明了布鲁埃对本文定义的岩石块的猜想。我们的方法涉及使用Kang-kashiwara-tsuchioka同构和kang-kashiwara-oh的kang-kashiwara-tsuchioka同构和分类方法转化为Quiver Hecke Superalgebras设置。结果，我们比有限群的块更通用的对象之间构建了莫里塔等同。特别是，我们的结果扩展到了一级环形元素超级甲壳虫的某些块。我们还研究了Quiver Hecke Superalgebras的假想性尖，并根据尖锐系统对箭量Hecke Superalgebras进行了不可约的表示。
We define and study RoCK blocks for double covers of symmetric groups. We prove that RoCK blocks of double covers are Morita equivalent to standard `local' blocks. The analogous result for blocks of symmetric groups, a theorem of Chuang and Kessar, was an important step in Chuang and Rouquier ultimately proving Broué's abelian defect group conjecture for symmetric groups. Indeed we prove Broué's conjecture for the RoCK blocks defined in this article. Our methods involve translation into the quiver Hecke superalgebras setting using the Kang-Kashiwara-Tsuchioka isomorphism and categorification methods of Kang-Kashiwara-Oh. As a consequence we construct Morita equivalences between more general objects than blocks of finite groups. In particular, our results extend to certain blocks of level one cyclotomic Hecke-Clifford superalgebras. We also study imaginary cuspidal categories of quiver Hecke superalgebras and classify irreducible representations of quiver Hecke superalgebras in terms of cuspidal systems.
