Related papers: From groups to symmetric spaces

We study spaces of matrices coming from irreducible representations of reductive groups over an algebraically closed field of characteristic zero and we completely classify those of constant corank one. In particular, we recover the…

The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a…

The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…

Ramsey algebras is an attempt to investigate Ramsey spaces generated by algebras in a purely combinatorial fashion. Previous studies have focused on the basic properties of Ramsey algebras and the study of a few specific examples. In this…

In this paper, we mainly discuss some generalized metric properties and the character of the free paratopological groups, and extend several results valid for free topological groups to free paratopological groups.

We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's…

The geometric realizations of Lusztig's symmetries of symmetrizable quantum groups are given in this paper. This construction is a generalization of that in [19].

A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.

We classify the irreducible projective representations of symmetric and alternating groups of minimal possible and second minimal possible dimensions, and get a lower bound for the third minimal dimension. On the way we obtain some new…

Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively. While recent approaches address this by explicitly…

An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…

An analogue of geometric quantization of Poisson algebras obtained by algebraic reduction of symmetries is developed. Interpretation of the obtained results and their application to the problem of commutativity of quantization and reduction…

We give another proof that a reductive algebraic group is geometrically reductive. We show that a quotient of the semi-stable locus (by a linear action of a reductive algebraic group on a projective scheme) exists, and from this Haboush's…

In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed…

We present a classification, up to isomorphisms, of all the homogeneous spaces of the Lorentz group with dimension lower than six. At the same time, we classify, up to conjugation, all the non-discrete closed subgroup of the Lorentz group…

Let $G$ be a Lie group, with an invariant non-degenerate symmetric bilinear form on its Lie algebra, let $\pi$ be the fundamental group of an orientable (real) surface $M$ with a finite number of punctures, and let $\bold C$ be a family of…

We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…

We discuss discrete Morrey spaces and their generalizations, and we prove necessary and sufficient conditions for the inclusion property among these spaces through an estimate for the characteristic sequences.

We initiate a careful study of a generalized symmetric imprimitivity theory for commuting proper actions of locally compact groups H and K on a C*-algebra.

In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we…