相关论文: On unitarizability and Arthur packets
We are lifting classical problems from single instances to regular sets of instances. The task of finding a positive instance of the combinatorial problem $P$ in a potentially infinite given regular set is equivalent to the so called…
In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical…
The combinatorial theory for the set of parity alternating permutations is expounded. In view of the numbers of ascents and inversions, several enumerative aspects of the set are investigated. In particular, it is shown that signed Eulerian…
An isomorphism between two hermitian unitals is proved, and used to treat isomorphisms of classical groups that are related to the isomorphism between certain simple real Lie algebras of types A and D (and rank 3).
In this paper we consider several classical and novel algorithmic problems for right-angled Artin groups, some of which are closely related to graph theoretic problems, and study their computational complexity. We study these problems with…
In this paper we generalize Cherednik's method and prove that certain Shimura varieties corresponding to groups of unitary similitudes and automorphic vector bundles over them have p-adic uniformization. This is proved for Shimura…
This is a survey article on classical groups (over arbitrary division rings) and their geometries.
Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.
We define cohomological complexes of locally compact abelian groups associated with varieties over $p$-adic fields and prove a duality theorem under some assumption. Our duality takes the form of Pontryagin duality between locally compact…
After a brief review of the idea and main results of the original p-adic string work, I describe the recent interest in p-adic strings in the context of AdS/CFT duality
The classical duality theory associates to an abelian group a dual companion. Passing to a non-abelian group, a dual object can still be defined, but it is no longer a group. The search for a broader category which should include both the…
We calculate extensions between certain irreducible admissible representations of p-adic groups.
In this paper, one proves an idea expressed by Clozel: inside an Arthur's packet, one has the representations in the Langlands' packet inside the Arthur's packet and more tempered representations than these representations
In his monograph (2013) Arthur characterizes the L-packets of quasisplit symplectic groups and orthogonal groups. By extending his work, we characterize the L-packets for the corresponding similitude groups with desired properties. In…
We study applications of a general approach for arities and arizabilities of theories to group and monoid theories. It is proved that a theory of a group $G$ is aritizable if and only if $G$ is finite. It is shown that this criterion does…
We investigate the Ulrich complexity of certain examples of Brauer--Severi varieties, twisted flags and involution varieties and establish lower and upper bounds. Furthermore, we relate Ulrich complexity to the categorical representability…
For a connected reductive group $G$ over ${\mathbb R}$, we study cohomological $A$-parameters, which are Arthur parameters with the infinitesimal character of a finite-dimensional representation of $G({\mathbb C})$. We prove a structure…
We investigate coherency properties of certain completed integral group rings, precisely for compact $p$-adic Lie groups.
In this note we, first, recall that the sets of all representatives of some special ordinary residue classes become $\left( m,n\right) $-rings. Second, we introduce a possible $p$-adic analog of the residue class modulo a $p$-adic integer.…
We describe all weights which are appropriated for the unitarization of linear representations of primitive partially ordered sets of finite type.