Related papers: Extraordinary dimension theories generated by comp…
We establish the existence of an irreducible representation of $A_n$ whose dimension does not occur as the dimension of an irreducible representation of $S_n$, and vice versa. This proves a conjecture by Tong-Viet. The main ingredient in…
We generalise the notions of supersymmetry and superspace by allowing generators and coordinates transforming according to more general Lorentz representations than the spinorial and vectorial ones of standard lore. This yields novel…
Chiral spinors and self dual tensors of the Lie superalgebra $\mathfrak{osp}(m|n)$ are infinite dimensional representations belonging to the class of representations with Dynkin labels $[0,\ldots,0,p]$. We have shown that the superdimension…
Using a first order Chern-Simons-like formulation of gravity we systematically construct higher-derivative extensions of general relativity in three dimensions. The construction ensures that the resulting higher-derivative gravity theories…
We give an introductory survey on the universal Vassiliev invariant called the perturbative series expansion of the Chern-Simons theory of links in euclidean space, and on its relation with the Kontsevich integral. We also prove an original…
In a previous paper, the authors introduced several vector space norms on the space of algebraic numbers modulo torsion which corresponded to the Mahler measure on a certain class of numbers and allowed the authors to formulate L^p Lehmer…
A dynamical system $(X,T)$ is \emph{shift embeddable} if $(X,T)$ embeds continuously and equivariantly in the shift over $[0,1]^d$ for some finite $d$. Refuting a major conjecture in the field, in a recent result of Dranishnikov and Levin…
We define two notions of discrete dimension based on the Minkowski and Hausdorff dimensions in the continuous setting. After proving some basic results illustrating these definitions, we apply this machinery to the study of connections…
We initiate a systematic study of intrinsic dimensional versions of classical functional inequalities which capture refined properties of the underlying objects. We focus on model spaces: Euclidean space, Hamming cube, and manifolds of…
We prove an analogue of a theorem of A. Pollington and S. Velani ('05), furnishing an upper bound on the Hausdorff dimension of certain subsets of the set of very well intrinsically approximable points on a quadratic hypersurface. The proof…
For an odd integer $r>0$ and an integer $n>r$, we introduce a notion of weakly $r$-separated collections of subsets of $[n]=\{1,2,\ldots,n\}$. When $r=1$, this corresponds to the concept of weak separation introduced by Leclerc and…
We propose and prove a new exact duality between the F-terms of supersymmetric gauge theories in five and three dimensions with adjoint matter fields. The theories are compactified on a circle and are subject to the Omega deformation. In…
In this paper we completely characterize all dimension functions on all models of the theory $T_{\log}$ of the asymptotic couple of the field of logarithmic transseries (Dimension Theorem). This is done by characterizing the "small"…
We introduce the concept of Gaussian integral isoperimetric transference and show how it can be applied to obtain a new class of sharp Sobolev-Poincar\'{e} inequalities with constants independent of the dimension. In the special case of…
In which a theory of dimension related to the Jones index and based on the notion of conjugation is developed. An elementary proof of the additivity and multiplicativity of the dimension is given and there is an associated trace.…
We give information about finite-dimensional Lie algebras and their representations for model building in 4 and 5 dimensions; e.g., conjugacy classes, types of representations, Weyl dimensional formulas, Dynkin indices, quadratic Casimir…
The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we establish a one to one correspondence between the set of…
We introduce the notion of Krull super-dimension of supermodules over certain super-commutative Noetherian super-rings. We investigate how this notion relates to the notion of odd regular sequence introduced by T.Schmitt and how it behaves…
A generic massive Thirring Model in three space-time dimensions exhibits a correspondence with a topologically massive bosonized gauge action associated to a self-duality constraint, and we write down a general expression for this…
We review the motivation and fundamental properties of the Hausdorff dimension of metric spaces and illustrate this with a number of examples, some of which are expected and well-known. We also give examples where the Hausdorff dimension…