代数群、有限群和量子群模的有界外延
Bounding Ext for modules for algebraic groups, finite groups, and quantum groups
摘要：
给定一个有限根系$Φ$，证明了存在一个整数$c=c(Φ)$，使得对任意具有根系$Φ$和任意不可约有理$G$ -模$L,L'$的约化代数群$G$，有$\dim\Ext_G^1(L,L')<c$.在李型有限群的情况下也有这样一个界，只依赖于根系而不依赖于基础域。对于量子群，对于任何整数$n\geq 0$，使用仅依赖于$n$和根系的常数，类似的结果对$\Ext^n$成立。较弱的版本，这是证明在代数和有限群的情况下，足以给类似的结果代数和一般的上同调。结果都使用，并有后果，Kazhdan-Lusztig多项式。附录证明了一个稳定的版本，需要小总理的论点，唐金的倾斜模猜想。
英文摘要：
Given a finite root system $Φ$, we show that there is an integer $c=c(Φ)$ such that $\dim\Ext_G^1(L,L')<c$, for any reductive algebraic group $G$ with root system $Φ$ and any irreducible rational $G$-modules $L,L'$. There also is such a bound in the case of finite groups of Lie type, depending only on the root system and not on the underlying field. For quantum groups, a similar result holds for $\Ext^n$, for any integer $n\geq 0$, using a constant depending only on $n$ and the root system. Weaker versions of this are proved in the algebraic and finite group cases, sufficient to give similar results for algebraic and generic cohomology. The results both use, and have consequences for, Kazhdan-Lusztig polynomials. An appendix proves a stable version, needed for small prime arguments, of Donkin's tilting module conjecture.
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