Related papers: Hidden sign in Langlands' correspondence
This paper has been withdrawn due to non-clearness of some technical points, as well as lack of a reasonable statement of quantization conjecture.
Why do natural and interesting sequences often turn out to be log-concave? We give one of many possible explanations, from the viewpoint of "standard conjectures". We illustrate with several examples from combinatorics.
We introduce a cryptographic method to hide an arbitrary secret payload in the response of a Large Language Model (LLM). A secret key is required to extract the payload from the model's response, and without the key it is provably…
Augmenting large language models (LLMs) with auxiliary tokens has emerged as a promising strategy for enhancing model performance. In this work, we introduce a lightweight method termed latent tokens; these are dummy tokens that may be…
This article presents a 3-local characterisation of the sporadic simple group McL and its automorphism group. The theorem is underpinned by a further identification theorem the proof of which is character theoretic. The main theorem is…
There has been a recent coming together of the Converse Theorem for $\gln$ and the Langlands-Shahidi method of controlling the analytic properties of automorphic $L$-functions which has allowed us to establish a number of new cases of…
Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…
Using an experimental work on "stopped light" as an example, we show how a classical phenomenon of linear optics - interference of polarized light - can imitate the effect of electromagnetically induced transparency.
Arc permutations, which were originally introduced in the study of triangulations and characters, have recently been shown to have interesting combinatorial properties. The first part of this paper continues their study by providing signed…
Apparently 'superluminal' transmission, e.g., in quantum tunnelling and its variants, occurs via a subtle interference mechanism which allows reconstruction of the entire spacial shape of a wave packet from its front tail. It is unlikely…
This is a report on the work of Robert Langlands, following his award of the Abel Prize in 2018. It includes his contributions to the general areas of Representation Theory, Automorphic Forms, Number Theory and Arithmetic Geometry. We have…
In a letter to Nature (Ford G W and O'Connell R F 1996 Nature 380 113) we presented a formula for the derivative of the hyperbolic cotangent that differs from the standard one in the literature by an additional term proportional to the…
We discuss the scenario with TeV-scale right-handed neutrinos, which are accessible at future colliders, while holding down tiny seesaw-induced masses and sizable couplings to the standard-model particles. The signal with tri-lepton final…
We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the…
Motivated by discrete Laplacian differential operators with various accuracy orders in numerical analysis, we introduce new matrices attached to a simple graph that can be considered graph Laplacians with higher accuracy. In particular, we…
In this article, we consider the links between parabolic induction and the local Langlands correspondence. We enunciate a conjecture about the (enhanced) Langlands parameters of supercuspidal representation of split reductives $p$-adics…
Langlands' beyond endoscopy proposal for establishing functoriality motivates interesting and concrete problems in the representation theory of algebraic groups. We study these problems in a setting related to the Langlands $L$-functions…
We modify the proof of the basic lemma of a paper of Saks and Zygmund on additive functions of rectangles.
The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables…
We show that, over a nonarchimedean local field, the rigid refined local Langlands correspondence and associated endoscopic character identities for connected reductive $G$ follow if one only has them for all such $G$ with connected center.…