Related papers: A Statement of the Fundamental Lemma

We give a general proof of Shahidi's tempered L-function conjecture, which has previously been known in all but one case. One of the consequences is the standard modules conjecture for p-adic groups, which means that the Langlands quotient…

We extend the results by R.P. Langlands on representations of (connected) abelian algebraic groups. This is done by considering characters into any divisible abelian topological group. With this we can then prove what is known as the…

The aim of these notes is to give an overview of several aspects of what has come to be called the relative Langlands program, a theme that takes its origin in the study of automorphic periods and their relations to particular cases of…

The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…

We state a conjecture, local Langlands in families, connecting the centre of the category of smooth representations on $\mathbb{Z}[\sqrt{q}^{-1}]$-modules of a quasi-split $p$-adic group $\mathrm{G}$ (where $q$ is the cardinality of the…

We give a simple proof of a crucial lemma that is established in [1, Lemma 2.1] by induction, and plays important roles in that paper and [2].

These notes deal with some basic notions related to p-adic numbers and functions of p-adic numbers.

In this article, we extend some results about algebra $A$ with the group of units $U(A)$ having a special polynomial identity, Laurent polynomial. And we present a new version of B. Hartley Conjecture with these identities.

This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is…

By a global approach, we prove the arithmetic fundamental lemma conjecture for unitary groups in $n$ variables over $\mathbb{Q}_p$ when $p\geq n$.

We give an elementary introduction, through illustrative examples but without proofs, to one of the basic consequences of the Langlands programme, namely the law governing the primes modulo which a given irreducible integral polynomial…

Probabilistic programming is considered as a framework, in which basic components of cognitive architectures can be represented in unified and elegant fashion. At the same time, necessity of adopting some component of cognitive…

In all forms of the local Langlands program the abelian category of smooth representations of p-adic groups G in vector spaces over a field k plays a central role. Of particular interest are its finiteness properties. If the field k has…

The Recognition Theorem for graded Lie algebras is an essential ingredient in the classification of finite-dimensional simple Lie algebras over an algebraically closed field of characteristic p > 3. The main goal of this monograph is to…

We study the homomorphisms between scalar generalized Verma modules. We conjecture that any homomorphism between is composition of elementary homomorphisms. The purpose of this article is to show the conjecture is affirmative for many…

This survey is meant to provide an introduction to the fundamental theorem of linear algebra and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to linear algebra. Specifically, we…

This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give…

In this letter, we provide new insight into Willems et al.'s fundamental lemma by studying the concept of universal inputs. An input is called universal if, when applied to any controllable system, it leads to input-output data that…

This erratum remedies errors in the literature pertaining to the stable Adams conjecture. As part of the above corrections, we also identify and fix two errors in section 4 of our recent article on the subject. We thank E. Fridelander for…

We define the notion of fundamental group of an algebraic stack, prove a comparison theorem between the fundamental group of a stack over the complex numbers and that of the associated analytic orbifold, show that this notion coincides with…