论文标题
在最大拆分案例中的感应性alperin-mckay条件下
On the Inductive Alperin-McKay Conditions in the Maximally Split Case
论文作者
论文摘要
Alperin-McKay猜想将$ \ ell $ block的高度零字符与其Brauer通讯员的高度相关联。第三作者，该猜想已减少到了准刺激组的所谓电感Alperin-McKay条件。这些条件仍然对谎言类型组开放。本文描述了$ \ ell $ - blocks中的高度零字符，当时$ \ ell $ divide $ q-1 $，在带有$ q $元素的字段上的谎言类型组。我们还提供有关$ \ ell $ -Blocks和Brauer通讯员的信息。作为一个申请，我们表明，$ \ mathbb {f} _q $ over $ c $的准简单组满足了Primes $ \ ell \ geq 5 $的归纳性alperin-mckay条件，并分配$ q-1 $。该末端的一些方法是根据Malle-späth的工作进行了改编的。
The Alperin-McKay conjecture relates height zero characters of an $\ell$-block with the ones of its Brauer correspondent. This conjecture has been reduced to the so-called inductive Alperin-McKay conditions about quasi-simple groups by the third author. Those conditions are still open for groups of Lie type. The present paper describes characters of height zero in $\ell$-blocks of groups of Lie type over a field with $q$ elements when $\ell$ divides $q-1$. We also give information about $\ell$-blocks and Brauer correspondents. As an application we show that quasi-simple groups of type $C$ over $\mathbb{F}_q$ satisfy the inductive Alperin-McKay conditions for primes $\ell\geq 5$ and dividing $q-1$. Some methods to that end are adapted from the work of Malle--Späth.
