Related papers: The Splitting Lemma in any Characteristic
The representation theory of semisimple algebraic groups over the complex numbers (equivalently, semisimple complex Lie algebras or Lie groups, or real compact Lie groups) and the question of whether a given representation is symplectic or…
A simple condition is given that is sufficient to determine whether a measure that is absolutely continuous with respect to a Gau{\ss}ian measure on the space of distributions is reflection positive. It readily generalises conventional…
For modular Lie superalgebras, new notions are introduced: Divided power homology and divided power cohomology. For illustration, we give presentations (in terms of analogs of Chevalley generators) of finite dimensional Lie (super)algebras…
Generalised indiscernibles highlight a strong link between model theory and structural Ramsey theory. In this paper, we use generalised indiscernibles as tools to prove results in both these areas. More precisely, we first show that a…
String theory and supersymmetry are theoretical ideas that go beyond the standard model of particle physics and show promise for unifying all forces. After a brief introduction to supersymmetry, we discuss the prospects for its experimental…
A family of formal power series, such that its coefficients satisfy a recursion formula, is characterized in terms of the summability, in the sense of J. P. Ramis, of its elements along certain well chosen directions. We describe a set of…
All the already known results on self descriptive numbers, together with the demonstration of the uniqueness for bases greater than 6, are here obtained through a systematic scheme of proof and not trial and error. The proof is also…
In the first part of the paper we prove a necessary and sufficient condition for the existence of the composition of formal power series in the case when the outer series is a series of one variable while the inner one is a series of…
We give a necessary condition for algebraicity of finite modules over the ring of formal power series. This condition is given in terms of local zero estimates. In fact we show that this condition is also sufficient when the module is a…
In this paper we generalise the notion of linearity (in the sense of Lawvere) to a category C equipped with a compatible sum structure and product structure. In this context, any morphism f from an n-fold sum to an n-fold product has a…
We introduce the definability strength of combinatorial principles. In terms of definability strength, a combinatorial principle is strong if solving a corresponding combinatorial problem could help in simplifying the definition of a…
This paper introduces the notion of a derived splinter. Roughly speaking, a scheme is a derived splinter if it splits off from the coherent cohomology of any proper cover. Over a field of characteristic 0, this condition characterises…
In an earlier preprint (math.AG/9810142) we gave an explicit description of the algebraic closure of the field of power series over a field of characteristic p, in terms of "generalized power series". In this paper, we give an analogous…
We give a new proof of the so-called Lie algebra version of Jacquet-Rallis's fundamental lemma for local non-Archimedean fields of characteristic zero. This proof is local and based on a previous result of W. Zhang on the compatibility of…
We say that $M$ and $S$ form a \textsl{splitting} of $G$ if every nonzero element $g$ of $G$ has a unique representation of the form $g=ms$ with $m\in M$ and $s\in S$, while $0$ has no such representation. The splitting is called {\it…
We provide a characterisation of differentially large fields in arbitrary characteristic and a single derivation in the spirit of Blum axioms for differentially closed fields. In the case of characteristic zero, we use these axioms to…
The elegance and usefulness of a complex formulation of the basic lensing equations is demonstrated with a number of applications. Using standard tools of complex function theory, we present, for instance, a new proof of the fact that the…
In this note, we describe a family of particular algebraic, and nonquadratic, power series over an arbitrary finite field of characteristic 2, having a continued fraction expansion with all partial quotients of degree one. The main purpose…
In this paper, we formulate the notion of split elements of a unipotent class in a connected reductive group $G$. Generalized Green functions of $G$ can be computed by using Lusztig's algorithm, if split elements exist for any unipotent…
We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields…