Using Harish-Chandra induction and restriction, we construct a categorical action of a Kac-Moody algebra on the category of unipotent representations of finite unitary groups in non-defining characteristic. We show that the decategorified representation is naturally isomorphic to a direct sum of level 2 Fock spaces. From our construction we deduce that the Harish-Chandra branching graph coincides with the crystal graph of these Fock spaces, solving a recent conjecture of Gerber-Hiss-Jacon. We also obtain derived equivalences between blocks, yielding Broué’s abelian defect group conjecture for unipotent \(\ell \)-blocks at linear primes \(\ell \).

使用Harish-Chandra归纳和限制，我们构造了一个Kac-Moody代数对非定义特征中有限unit群的单能表示类别的分类作用。我们表明，已分类的表示对于2级Fock空间的直接和是自然同构的。根据我们的构造，我们推断出Harish-Chandra分支图与这些Fock空间的晶体图重合，从而解决了Gerber-Hiss-Jacon的一个新猜想。我们还获得了块之间的导出等价性，从而得出了线性素数\（\ ell \）下单能\（\ ell \）-块的Broué阿贝尔缺陷群猜想。