标题： 仿射Hecke代数具有不相等参数的几何实现 显示英文标题

标题： Geometric realizations of affine Hecke algebras with unequal parameters

摘要： 我们给出了所有具有两个不相等参数的仿射赫克代数的$K$理论实现，包括例外类型。 这扩展了Kazhdan和Lusztig的著名工作，他们给出了具有相等参数的仿射赫克代数的$K$理论实现，并补充了Kato的结果，他将这种构造推广到了三参数仿射赫克代数类型$C$。 我们新构造背后的关键思想是利用小特征下的伴随表示的可约性。 我们还证明，在适当的几何条件下，我们的构造可以导致简单模的Deligne-Langlands风格分类。 我们验证了$G_2$的这些几何条件，从而得到了两个参数的仿射赫克代数$G_2$在非单位根处的完整几何分类。 显示英文摘要

摘要： We give a $K$-theoretic realization of all affine Hecke algebras with two unequal parameters including exceptional types. This extends the celebrated work of Kazhdan and Lusztig, who gave a $K$-theoretic realization of affine Hecke algebras with equal parameters, and complements results of Kato, who extended this construction to the three-parameter affine Hecke algebra of type $C$. A key idea behind our new construction is to exploit the reducibility of the adjoint representation in small characteristic. We also show that under suitable geometric conditions, our construction leads to a Deligne-Langlands style classification of simple modules. We verify these geometric conditions for $G_2$ thereby obtaining a full geometric classification of the simple modules for the affine Hecke algebra of $G_2$ with two parameters away from roots of unities.