论文标题
关于唐金的倾斜模块猜想III：新的通用下限
On Donkin's Tilting Module Conjecture III: New Generic Lower Bounds
论文作者
论文摘要
在本文中，作者考虑了还原性代数群体的代表理论的四个主要兴趣问题：（i）唐金的倾斜模块猜想，（ii）Humphreys-Verma问题，（iii）$ \ operatatorname {st} _r \ otime l \ otime l（λ）$ y（λ）$ l（λ）$ l（λ）是$ l（lir for $ l（λ） $p^{r}$-restricted highest weight, and (iv) whether $\operatorname{Ext}^{1}_{G_{1}}(L(λ),L(μ))^{(-1)}$ is a tilting module where $L(λ)$ and $L(μ)$ have $p$-restricted highest weight. 作者用新的统一绑定为每个问题建立了肯定的答案，即$ p \ geq 2h-4 $，其中$ h $是coxeter编号。值得注意的是，这将验证这些陈述的无限案例。在本文的稍后，考虑了两组的问题（i） - （iv），其中有反述（小素数）。
In this paper the authors consider four questions of primary interest for the representation theory of reductive algebraic groups: (i) Donkin's Tilting Module Conjecture, (ii) the Humphreys-Verma Question, (iii) whether $\operatorname{St}_r \otimes L(λ)$ is a tilting module for $L(λ)$ an irrreducible representation of $p^{r}$-restricted highest weight, and (iv) whether $\operatorname{Ext}^{1}_{G_{1}}(L(λ),L(μ))^{(-1)}$ is a tilting module where $L(λ)$ and $L(μ)$ have $p$-restricted highest weight. The authors establish affirmative answers to each of these questions with a new uniform bound, namely $p\geq 2h-4$ where $h$ is the Coxeter number. Notably, this verifies these statements for infinitely many more cases. Later in the paper, questions (i)-(iv) are considered for rank two groups where there are counterexamples (for small primes) to these questions.
