Corina Ciobotaru
By employing a new strategy we prove that all parabolically induced unitary representations of the Burger-Mozes universal group U(F)^+, with F being primitive, have all their matrix coefficients vanishing at infinity. This generalizes the same well-known result for the universal group U(F)^+, when F is 2-transitive.
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In this paper, we consider representations of $p$-adic classical groups parabolically induced from the products of shifted Speh representations and unitary representations of Arthur type of good parity. We describe how to compute the socles (the maximal semisimple subrepresentations) of these representations. As a consequence, we can determine whether these representations are reducible or not. In particular, our results produce many unitary representations, which are called complementary series.
Irreducibility criterion for representations induced by essentially unitary ones (case of non-archimedean GL(n,A)
设A是局部非阿基米德域F上的有限维中心除代数。固定GL（n，A）的任意抛物子群P和P的一个Levi因子M，设π是M的一个不可约酉表示和M的一个特征标.给出了GL（n，A）的抛物诱导表示Ind（π）不可约的一个显式充要条件.
We explicitly construct the structure of Jacquet modules of parabolically induced representations of even unitary groups and even general unitary groups over a $p$-adic field $F$ of characteristic different than two. As an application, we obtain a classification of strongly positive discrete series representations of those groups.
We study a problem concerning parabolic induction in certain p-adic unitary groups. More precisely, for $E/F$ a quadratic extension of p-adic fields the associated unitary group $G=\mathrm{U}(n,n)$ contains a parabolic subgroup $P$ with Levi component $L$ isomorphic to $\mathrm{GL}_n(E)$. Let $π$ be an irreducible supercuspidal representation of $L$ of depth zero. We use Hecke algebra methods to determine when the parabolically induced representation $ι_P^G π$ is reducible.
On reducibility of induced representations of odd unitary groups: the depth zero case
本文研究 $p$-adic 酉群中抛物诱导表示的可约性，针对深度为零的不可约超尖表示，利用 Hecke 代数方法给出判定条件。
We study the parabolically induced complex representations of the unitary group in 5 variables, $ U(5), $ defined over a p-adic field. Let $F$ be a p-adic field. Let $E : F$ be a field extension of degree two. Let $Gal(E : F ) = \{ 1, σ\}.$ We write $ σ(x) = \overline{x} \; \forall x \in E. $ Let $ E^* := E \setminus \{ 0 \} $ and let $ E^1 := \{x \in E \mid x \overline{x} = 1 \}$. $U(5) $ has three proper standard Levi subgroups, the minimal Levi subgroup $ M_0 \cong E^* \times E^* \times E^1 $ and the two maximal Levi subgroups $ M_1 \cong GL(2, E) \times E^1 $ and $ M_2 \cong E^* \times U(3…
R-groups and parameters
对于典型群，我们显示的Knapp-Stein $R$ -组，它描述了结构的抛物线诱导表示，和阿瑟$R$ -组的参数相关的诱导表示的局部朗兰兹猜想的同构。我们这样做的情况下，从离散系列表示归纳。在酉群的情况下，我们表明这种同构下的参数，我们显示持有至少一半的情况下，一个温和的假设。
Let $\mathbf{G}$ be an unramified quasi-split unitary group over a p-adic field of odd residual characteristic. The goal of this paper is to describe the supercuspidal representations within certain L-packets of $\mathbf{G}$, which are classified by Arthur and Mok using the theory of endoscopy. The description is given in terms of the cuspidal types constructed by Bushnell-Kutzko and Stevens. As a starting example, we require the parameters of our packets to satisfy certain regularity conditions, such that these packets consist of very cuspidal representations in the sense of Adler and Reeder.…
In the first part of the paper we give some bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical p-adic groups. Roughly, it can show up only if the central character of the inducing irreducible cuspidal representation is dominated in an appropriate way by the square root of the modular character of minimal parabolic subgroup. For representations supported by fixed parabolic subgroup, a more precise bound is given. There are also bounds for specific Bernstein components. A number of these upper bounds are best possible. Th…
On local coefficients for non-generic representations of some classical groups
本文研究了非阿基米德局部域上的分裂正交群和拟分裂酉群的表示，它们不是一般的，而是支持一个不同类型的唯一模型，即广义贝塞尔模型.研究了Bessel模型在归纳下的性质，证明了在适当意义下极小的Bessel模型与Rodier关于Whittaker模型的归纳定理类似.建立了Bessel泛函的诱导参数的全纯性。最后，局部系数被定义为每个不可约的超尖点表示进行贝塞尔功能，也为一定的组成部分，每个代表抛物线诱导从这样的超尖点。
Irreducibility of the parabolic induction of essentially Speh representations and a representation of Arthur type over a p-adic field
本文证明了p-adic域上本质Speh表示与Arthur型表示的抛物诱导不可约性当且仅当特定子诱导不可约，并确定了Speh表示诱导的合成列，构造出新的酉表示。
Unitary representations of the universal cover of SU(1,1) and tensor products
本文研究了单李代数的权模与相应的单连通李群的酉表示之间的关系。特别是我们认为详细从这个角度来看，SU（1，1）的泛覆叠群，包括新的结果的离散部分的张量积的不可约表示。作为这些结果的结果，我们表明，一组光滑的向量的张量积相交平凡的离散谱中的一些表示。
We study the parabolically induced complex representations of the unitary group in 5 variables, $ U(5), $ defined over a p-adic field. Let $ F $ be a p-adic field. Let $ E : F $ be a field extension of degree two. Let $ Gal(E : F ) = \{ 1 , σ\}. $ We write $ σ(x) = \overline{x} \; \forall x \in E. $ Let $ E^* := E \setminus \{ 0 \} $ and let $ E^1 := \{x \in E \mid x \overline{x} = 1 \}. $ $ U(5) $ has three proper standard Levi subgroups, the minimal Levi subgroup $ M_0 \cong E^* \times E^* \times E^1 $ and the two maximal Levi subgroups $ M_1 \cong GL(2, E) \times E^1 $ and $ M_2 \cong E^* \…
Let $G_{\mathbb{R}}$ be a real reductive Lie group and $G'_{\mathbb{R}}$ a reductive subgroup of $G_{\mathbb{R}}$ such that $\mathfrak{g'}$ is algebraic in $\mathfrak{g}$. In this paper, we consider restrictions of irreducible representations of $G_{\mathbb{R}}$ to $G'_{\mathbb{R}}$ and induced representations of irreducible representations of $G'_{\mathbb{R}}$ to $G_{\mathbb{R}}$. Our main concern is when such a representation has uniformly bounded multiplicities, i.e. the multiplicities in the representation are (essentially) bounded. We give characterizations of the uniform boundedness by p…
Zero patterns and unitary similarity
无迹复$n\times n$矩阵的空间L（n）的子空间可以通过要求某些位置$(i,j)$处的项为零来指定。这些位置的集合$I$是（零）模式，并且L（n）的对应子空间由$L_I(n)$表示。一个模式$I$是泛模式，如果L（n）中的每个矩阵都与$L_I(n)$中的某个矩阵酉相似.提出了描述通用模式的问题，并对$n\le3$完全解决了这个问题，对$n=4$也得到了部分结果.构造了两个无限族的泛模式。它们给出了舒尔三角化定理的两个类似物。
On the classification of unitary highest weight modules in the exceptional cases
本文利用Dirac不等式和PRV积，完成了例外李群$SO_e(2,n)$、$E_{6(-14)}$和$E_{7(-25)}$的万有覆盖的酉最高权模分类，并描述了给定无穷小特征的此类模。
Positive definite superfunctions and unitary representations of Lie supergroups
对一类广泛的Frechet-Lie超群，证明了正定光滑超函数与酉表示的矩阵系数之间存在对应关系.给出了对应于解析酉表示的矩阵系数的泛包络代数上的线性泛函的特征。
Free unitary groups are (almost) simple
我们证明了Wang和Van Daele的泛量子群的中心子群是单的，因为它们没有正规量子子群，从而提供了具有非对易熔合环的简单紧量子群的第一个例子.
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