论文标题
GL_2的通用和mod p kazhdan-lusztig理论
Generic and Mod p Kazhdan-Lusztig Theory for GL_2
论文作者
论文摘要
令$ f $为一个非架构的本地字段，其残基字段$ \ mathbb {f} _q $，让$ g = gl_ {2/f} $。令$ \ mathbf {q} $成为不确定的，让$ h^{（1）}（\ Mathbf {q}）$为$ g（f）$ g（f）$的通用pro-p iwahori-hecke代数。令$ v _ {\ wideHat {g}} $为双组$ \ widehat {g} $的Vinberg monoid。我们为Kazhdan-Lusztig-Ginzburg球形表示，Bernstein Map和satake Isomormorphism建立了$ H^{（1）}（\ Mathbf {Q}）$的通用版本。我们为monoid $ v _ {\ wideHat {g}} $定义标志品种，并在其equivariant k理论中建立特征图。这些通用构造在专业化$ \ mathbf {q} = q \ in \ mathbb {c} $之后恢复了经典构造。在$ \ mathbf {q} = q = 0 \ in \ overline {\ mathbb {f}} _ q $，球形地图提供了所有不可回值的$ h^{（1）} _ {\ edline {\ edline {\ mathbb {f} {f} _ q} _ Q}（0）的双重参数化。
Let $F$ be a non-archimedean local field with residue field $\mathbb{F}_q$ and let $G = GL_{2/F}$. Let $\mathbf{q}$ be an indeterminate and let $H^{(1)}(\mathbf{q})$ be the generic pro-p Iwahori-Hecke algebra of the group $G(F)$. Let $V_{\widehat{G}}$ be the Vinberg monoid of the dual group $\widehat{G}$. We establish a generic version for $H^{(1)}(\mathbf{q})$ of the Kazhdan-Lusztig-Ginzburg spherical representation, the Bernstein map and the Satake isomorphism. We define the flag variety for the monoid $V_{\widehat{G}}$ and establish the characteristic map in its equivariant K-theory. These generic constructions recover the classical ones after the specialization $\mathbf{q} = q \in \mathbb{C}$. At $\mathbf{q} = q = 0 \in\overline{\mathbb{F}}_q$, the spherical map provides a dual parametrization of all the irreducible $H^{(1)}_{\overline{\mathbb{F}}_q}(0)$-modules.
