论文标题
Mackey型的身份，用于有限统一组的谎言代数和应用
Mackey-type identity for invariant functions on Lie algebras of finite unitary groups and an application
论文作者
论文摘要
标题中提到的Mackey型身份将抛物线诱导的操作和对有限统一组$ u（n，q^2）$的LIE代数的不变功能的限制。如作者论文中介绍的那样，该结果应用于在带有负霍尔小木参数的新的分支图上构建正谐波函数[adv。数学。卷。 395（2022），108087; ARXIV：2102.01947]。这反过来意味着存在着无限参数的不变措施家族，用于$ u（n，q^2）$的无限二维类似物的共连接作用。
The Mackey-type identity mentioned in the title relates the operations of parabolic induction and restriction for invariant functions on the Lie algebras of the finite unitary groups $U(N, q^2)$. This result is applied to constructing positive harmonic functions on a new branching graph with a negative Hall-Littlewood parameter, as introduced in the authors' paper [Adv. Math. vol. 395 (2022), 108087; arXiv:2102.01947].This in turn implies the existence of an infinite-parameter family of invariant measures for the coadjoint action of an infinite-dimensional analogue of the groups $U(N, q^2)$.
