Related papers: On the dimension datum of a subgroup. II
In this paper we show three new results concerning dimension datum. Firstly, for two subgroups $H_{1}$($\cong U(2n+1)$) and $H_{2}$($\cong Sp(n)\times SO(2n+2)$) of $SU(4n+2)$, we find a family of pairs of irreducible representations…
The dimension datum of a closed subgroup of a compact Lie group is the sequence of invariant dimensions of irreducible representations by restriction. In this article we classify closed connected subgroups with equal dimension data or…
The dimension datum of a closed subgroup of a compact Lie group is a sequence by assigning the invariant dimension of each irreducible representation restricting to the subgroup. We prove that any sequence of dimension data contains a…
We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural `dimension pair'. In particular, we compute these dimensions for certain classes of self-affine sets and quasi-self-similar sets…
We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that…
We first briefly review some aspects of the techniques of dealing with ultraviolet divergences in Feynman amplitudes in an Euclidian $D$-dimensional space-time. Next we consider compactification of a $d$-dimensional ($d\leq D$) subspace.…
We present two approaches, one homological and the other simplicial, for the investigation of dimension quotients of groups. The theory is illustrated, in particular, with a conceptual discussion of the fourth and fifth dimension quotients.
Duality groups of Abelian gauge theories on four manifolds and their reduction to two dimensions are considered. The duality groups include elements that relate different space-times in addition to relating different gauge-coupling…
Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…
This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…
With each piecewise monotonic map of the unit interval, a dimension triple is associated. The dimension triple, viewed as a Z[t, t^{-1}] module, is finitely generated, and generators are identified. Dimension groups are computed for Markov…
We study some aspects when one consider the existence of one extra-dimension in addition to a non-commutative space-time. We present here two different examples, where the first one provides a scenario were it is possible to relate the…
We consider the notion of dimension in four categories: the category of (unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and the category of (unbounded) separable metric spaces and (metrically proper) uniform…
According to modern quantum physics, at the microlevel, the dimension of space-time is at least 11; we only observe 4 dimensions because the others are compactified: the size along each of the other dimensions is much smaller than the…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…
A string theory in $3$ euclidean spacetime dimensions is found to describe the semiclassical behavior of a certain exact physical state of quantum general relativity in $4$ dimensions. Both the worldsheet and the three dimensional metric…
This is a detailed introductory survey of the cohomological dimension theory of compact metric spaces.
We review some aspects of theories with compact extra dimensions. We consider the motivation and the theoretical basis of Large, Universal and Warped Extra Dimensions. We focus on those aspects that are potentially relevant in the…
We discuss a systematic way to dimensionally regularize divergent sums arising in field theories with an arbitrary number of physical compact dimensions or finite temperature. The method preserves the same symmetries of the action as the…
The methods of Information geometry have been glowing up to develop various subjects of theoretical physics, including quantum information systems. The present article has two purposes. The first one is to develop general theory of…