相关论文: Embeddings of the symmetric groups to the space Cr…

In this note we describe the embeddings of the Heisenberg group into the Cremona group.

We survey the theory of totally symmetric sets, with applications to homomorphisms of symmetric groups, braid groups, linear groups, and mapping class groups.

We initiate the study of analogues of symmetric spaces for the family of finite dihedral groups. In particular, we investigate the structure of the automorphism group, characterize the involutions of the automorphism group, and determine…

In this paper we examine various properties/constructions which are known for reductive groups and we do some experiments to see to what extent they generalize to symmetric spaces.

We describe the Morse groups of the nearby cycles sheaves on the nilcones in three classical symmetric spaces.

We show that certain groups of diffeomorphisms and PL-homeomorphisms embed in the group of all quasi-isometries of the Euclidean spaces.

We classify the symmetric association schemes with faithful spherical embedding in 3-dimensional Euclidean space. Our result is based on previous research on primitive association schemes with $m_1 = 3$.

The first group of results of this paper concerns the compressibility of finite subgroups of the Cremona groups. The second concerns the embeddability of other groups in the Cremona groups and, conversely, the Cremona groups in other…

In this paper, we investigate the structure of associated groups of symmetric quandles. Among other results, we explore the relationship between the associated group of a symmetric quandle and that of its underlying quandle. We provide a…

Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…

We classify $R$-spaces that admit a certain natural $\Gamma$-symmetric structure. We further determine the maximal antipodal sets of these structures.

For a rational elliptic space, this paper examines the relationship between its homotopy groups and its self-homotopy equivalence group. Moreover, we investigate how this group is embedded in general linear groups.

We study the restriction to the symmetric group, $\mc{S}_n$ of the adjoint representation of $\mt{GL}_n(\C)$. We determine the irreducible constituents of the space of symmetric as well as the space of skew-symmetric $n\times n$ matrices as…

In this paper we use the group of mirror symmetries for the construction of the vector fields on spheres.

We completely describe inhomogeneous properly embedded almost symmetric submanifolds of Euclidean space as certain unions of parallel symmetric submanifolds of the ambient Euclidean space.

Every compact symmetric space $M$ admits a dual noncompact symmetric space $\check{M}$. When $M$ is a generalized Grassmannian, we can view $\check{M}$ as a open submanifold of it consisting of space-like subspaces \cite{HL}. Motivated from…

In this paper we generalize a result in [1], showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of…

We study symplectic groups and indefinite orthogonal groups over involutive, possibly noncommutative, algebras $(A, \sigma)$. In the case when the algebra $(A, \sigma)$ is Hermitian, or the complexification $(A_{\mathbb{C}},…

The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…

We describe the conformal symmetries of asymptotically flat spacetime. These represent an extension of the BMS group that we call the conformal BMS group. Its general features are discussed.