Related papers: Dualities for root systems with automorphisms and …

In this article, we are concerned with the Langlands functoriality conjecture. Cogdell, Kim, Piatetski-Shapiro and Shahidi proved functioriality conjecture in the case of a globally generic cuspidal automorphic representation for the split…

Motivated by Lang-Vojta's conjecture, we show that the set of dominant rational self-maps of an algebraic variety over a number field with only finitely many rational points in any given number field is finite by combining Amerik's theorem…

The foundations of Ringel duality for split quasi-hereditary algebras over commutative Noetherian rings are strengthened. Several descriptions and properties of the smallest resolving subcategory containing all standard modules over split…

We consider the structure of groups and algebras that can be represented as automorphisms or derivations of distributive products -- which includes nonassociative rings, modules, forms, and commutation of groups and nonassociative loops. In…

We systematically analyze backgrounds that are holographic duals to non-relativistic CFTs, by constructing them as cosets of the Schrodinger group and variants thereof. These cosets G/H are generically non-reductive and we discuss in…

Brylinski and Deligne have provided a framework to study central extensions of reductive groups by K2 over a field F. Such central extensions can be used to construct central extensions of p-adic groups by finite cyclic groups, including…

We consider infinite connected quasi-transitive locally finite graphs and show that every such graph with more than one end is a tree amalgamation of two other such graphs. This can be seen as a graph-theoretical version of Stallings'…

We study the structure of generalized Baumslag-Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of…

We explore some connections between vectors of integers and integer partitions seen as bi-infinite words. This methodology enables us to give a combinatorial interpretation of the Macdonald identities for affine root systems of the seven…

We characterize those Lie groups, and algebraic groups over a local field of characteristic zero, whose first reduced L^p-cohomology is zero for all p>1, extending a result of Pansu. As an application, we obtain a description of…

Let $\Delta$ be a rank 2 hyperbolic root system. Then $\Delta$ has generalized Cartan matrix $H(a,b)= \left(\begin{smallmatrix} ~2 & -b\\ -a & ~2 \end{smallmatrix}\right)$ indexed by $a,b\in\mathbb{Z}$ with $ab\geq 5$. If $a\neq b$, then…

The purpose of this paper is to generalise Sullivan's rational homotopy theory to non-nilpotent spaces, providing an alternative approach to defining Toen's schematic homotopy types over any field k of characteristic zero. New features…

A generalization of down-up algebras was introduced by Cassidy and Shelton (J. Algebra 279 (2004), no. 1), the so-called generalized down-up algebras. We describe the automorphism group of conformal Noetherian generalized down-up algebras…

We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…

We consider rational projective homogeneous varieties over an algebraically closed field of positive characteristic, namely quotients of a semi-simple group by a possibly non-reduced parabolic subgroup. We determine the group scheme…

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…

The general features of the degeneracy structure of ($p=2$) parasupersymmetric quantum mechanics are employed to yield a classification scheme for the form of the parasupersymmetric Hamiltonians. The method is applied to parasupersymmetric…

If K is a number field, arithmetic duality theorems for tori and complexes of tori over K are crucial to understand local-global principles for linear algebraic groups over K. When K is a global field of positive characteristic, we prove…

Formulating gauge theories for gauge groups admitting a continuous center can require to include charged scalars to define a gauge-coupling function. We show that the gauge-fields in the center can be dualized into form-fields of…

An important property of a Hopf algebra is its quasitriangularity and it is useful various applications. This property is investigated for quantum groups $sl_2$ at roots of 1. It is shown that different forms of the quantum group $sl_2$ at…