Related papers: On the intersection of local Arthur packets for cl…

Region extraction is a very common task in both Computer Science and Engineering with several applications in object recognition and motion analysis, among others. Most of the literature focuses on regions delimited by straight lines, often…

Let $G$ be a classical group $\GL(n)$, $\oU(n)$, $\oO(n)$ or $\Sp(2n)$, over a non-archimedean local field of characteristic zero. Let $\pi$ be an irreducible admissible smooth representation of $G$. It is well known that the contragredient…

We extend the relative theory of admissible pairs and $p$-adic Hodge structures introduced in Part II to allow variation in the underlying local systems of $\mathbb{Q}_p$-vector spaces and isocrystals. This extension accommodates, in…

Let $F$ be a non-Archimedean local field with odd characteristic $p$. Let $N$ be a positive integer and $G=Sp_{2N}(F)$. By work of Lomel\'i on $\gamma$-factors of pairs and converse theorems, a generic supercuspidal representation $\pi$ of…

We study the design of robust subexponential algorithms for classical connectivity problems on intersection graphs of similarly sized fat objects in $\mathbb{R}^d$. In this setting, each vertex corresponds to a geometric object, and two…

In this paper, we give a simple and short proof of the uniqueness of generic representations in an $L$-packet for a quasi-split connected classical group over a non-archimedean local field.

We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and…

We classify what we call ``typically almost symmetric'' depth zero supercuspidal representations of classical groups into L-packets. Our main results resolve an ambiguity in the paper of Lust-Stevens \cite{Lust-Stevens} in this case, where…

Message passing equations yield a sharp percolation transition in finite graphs, as an artifact of the locally treelike approximation. For an arbitrary finite, connected, undirected graph we construct an infinite tree having the same local…

The problem deals with an exact calculation of the intersection area of a circle arbitrary placed on a grid of square shaped elements with gaps between them (finite fill factor). Usually an approximation is used for the calculation of the…

We consider the eigenvalue problem and the associated intersection theory of homogenous spaces for the symplectic and odd orthogonal groups. We solve the Horn and saturation problems for these classical groups.

We study the Steiner Tree problem on the intersection graph of most natural families of geometric objects, e.g., disks, squares, polygons, etc. Given a set of $n$ objects in the plane and a subset $T$ of $t$ terminal objects, the task is to…

In this paper, we prove, following earlier work of Waldspurger ([Wa1], [Wa4]), a sort of local relative trace formula which is related to the local Gan-Gross-Prasad conjecture for unitary groups over a local field $F$ of characteristic…

We consider the symplectic group $\mathrm{Sp}_{2n}$ defined over a $p$-adic field $F$, where $p=2$. We prove that every simple supercuspidal representation (in the sense of Gross--Reeder) of $\mathrm{Sp}_{2n}(F)$ corresponds to an…

We are concerned with the problem of designing large families of subsets over a common labeled ground set that have small pairwise intersections and the property that the maximum discrepancy of the label values within each of the sets is…

Let G be the group of rational points of a quasi-split p-adic special orthogonal, symplectic or unitary group for some odd prime number p. FollowingArthur and Mok, there are a positive integer N, a p-adic field E and a local functorial…

We study vertex-ordering problems in loop-free digraphs subject to constraints on the left-going arcs, focusing on existence conditions and computational complexity. As an intriguing special case, we explore vertex-specific lower and upper…

For an essentially tame supercuspidal representation $\pi$ of a connected reductive $p$-adic group $G$, we establish two distinct and complementary sufficient conditions for the irreducible components of its restriction to a maximal compact…

Let $F$ be a non-archimedean local field of characteristic different from $2$ and $G$ be either an odd special orthogonal group ${\rm SO}_{2r+1}(F)$ or a symplectic group ${\rm Sp}_{2r}(F)$. In this paper, we establish the local converse…

In this paper, we introduce a notion of ladder representations for split odd special orthogonal groups and symplectic groups over a non-archimedean local field of characteristic zero. This is a natural class in the admissible dual which…