论文标题
对Hecke代数分类为统一根源，第一部分
Categorifying Hecke algebras at prime roots of unity, part I
论文作者
论文摘要
我们为Type $ a $ diagrammatic Hecke类别配备了特殊的推导，因此在专业化特征$ p $之后，它将成为$ p $ -DG类别。我们证明，Hecke代数的定义关系在$ p $ -DG GROTHENDIECK集团中得到满足。我们推测，$ p $ -DG GROTHENDIECK Group对Iwahori-Hecke代数是同构的，它为其提供了与Kazhdan-Lusztig基础和$ P $ p $ nosical-noonical基础的基础。更精确的猜想将在续集中找到。 以下是本文中包含的其他一些结果。我们提供了图形Hecke类别中所有度量$+2 $衍生的分类的不完整证明，以及在$ p $ -DG -DG GROTHENDIECK集团中满足Hecke代数的这些派生关系的完全证明。特别是，我们的特殊派生是二元性和等效性的独特之处。我们证明，在有限和仿射类型$ a $之外简单的类型中不存在这种推导。我们还检查了特定的bott-samelson bimodule $ a_7 $，在特征$ 2 $中是不可分解的，但在所有其他特征中都可以分解。我们证明，这种Bott-Samelson Bimodule在任何特征中都没有承认任何不平凡的奇妙过滤，这是$ p $ -DG的类似物，是不可分解的。
We equip the type $A$ diagrammatic Hecke category with a special derivation, so that after specialization to characteristic $p$ it becomes a $p$-dg category. We prove that the defining relations of the Hecke algebra are satisfied in the $p$-dg Grothendieck group. We conjecture that the $p$-dg Grothendieck group is isomorphic to the Iwahori-Hecke algebra, equipping it with a basis which may differ from both the Kazhdan-Lusztig basis and the $p$-canonical basis. More precise conjectures will be found in the sequel. Here are some other results contained in this paper. We provide an incomplete proof of the classification of all degree $+2$ derivations on the diagrammatic Hecke category, and a complete proof of the classification of those derivations for which the defining relations of the Hecke algebra are satisfied in the $p$-dg Grothendieck group. In particular, our special derivation is unique up to duality and equivalence. We prove that no such derivation exists in simply-laced types outside of finite and affine type $A$. We also examine a particular Bott-Samelson bimodule in type $A_7$, which is indecomposable in characteristic $2$ but decomposable in all other characteristics. We prove that this Bott-Samelson bimodule admits no nontrivial fantastic filtrations in any characteristic, which is the analogue in the $p$-dg setting of being indecomposable.
