GL_2的通有和Mod p Kazhdan-Lusztig理论
Generic and Mod p Kazhdan-Lusztig Theory for GL_2
摘要：
设$F$是具有剩余域$\mathbb{F}_q$的非阿基米德局部域，设$G = GL_{2/F}$。设$\mathbf{q}$是不定式，$H^{(1)}(\mathbf{q})$是群$G(F)$的泛pro-p Iwahori-Hecke代数.设$V_{\widehat{G}}$是对偶群$\widehat{G}$的Vinberg幺半群.我们建立了一个通用版本的$H^{(1)}(\mathbf{q})$的Kazhdan-Lusztig-Ginzburg球面表示，伯恩斯坦映射和佐竹同构。定义了么半群$V_{\widehat{G}}$的旗簇，并建立了其等变K-理论的特征映射。这些类属结构在特殊化$\mathbf{q} = q \in \mathbb{C}$之后恢复了经典类属结构。在$\mathbf{q} = q = 0 \in\overline{\mathbb{F}}_q$，球面映射提供了所有不可约$H^{(1)}_{\overline{\mathbb{F}}_q}(0)$ -模的对偶参数化。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
