Related papers: From groups to symmetric spaces

We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. In a previous paper we have shown that the inclusion of the first space into the second one is a homotopy…

Riemannian and pseudo-Riemannian symmetric spaces with semisimple transvection group are known and classified for a long time. Contrary to that the description of pseudo-Riemannian symmetric spaces with non-semisimple transvection group is…

Several problems in number theory when reformulated in terms of homogenous dynamics involve study of limiting distributions of translates of algebraically defined measures on orbits of reductive groups. The general non-divergence and…

In this paper we study the space of morphisms from a complex projective space to a compact smooth toric variety X. It is shown that the first author's stability theorem for the spaces of rational maps from CP^m to CP^n extends to the spaces…

Let V be a unitary space. Suppose G is a subgroup of the full symmetric group S_m and X is an irreducible unitary representation of G. In this paper, we introduce the generalized Cartesian symmetry class over V associated with G and X. Then…

We explain some simple methods to establish the property of Rapid Decay for a number of groups arising geometrically. We also give new examples of groups with the property of Rapid Decay. In particular we establish the property of Rapid…

The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory - harmonic analysis for noncommutative groups with infinite-dimensional dual space. I omitted detailed proofs but tried…

Symmetric cohomology of groups, defined by M. Staic in [2], is similar to the way one defines the cyclic cohomology for algebras. We show that there is a well-defined restriction, conjugation and transfer map in symmetric cohomology, which…

Retraction maps have been generalized to discretization maps in (Barbero Li\~n\'an and and Mart\'{\i}n de Diego, 2022). Discretization maps are used to systematically derive numerical integrators that preserve the symplectic structure, as…

This paper is devoted to the study of isometrically homogeneous spaces from the view point of metric geometry. Mainly we focus on those spaces that are homeomorphic to lines. One can reduce the study to those distances on $\R$ that are…

We introduce geometric quantization in the setting of shifted symplectic structures. We define Lagrangian fibrations and prequantizations of shifted symplectic stacks and their geometric quantization. In addition, we study many examples…

We prove various results connecting structural or algebraic properties of graphs and groups to conditions on their spaces of harmonic functions. In particular: we show that a group with a finitely supported symmetric measure has a…

We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…

Semistable reduction theorem for projective morphisms in the category of complex analytic spaces is established.

The article contains a survey of results on length-commensurable and isospectral locally symmetric spaces and related problems in the theory of semi-simple algebraic groups.

This is a preliminary version of the first chapter of a book project on the character theory of finite groups of Lie type. It provides the foundations from the general theory of reductive algebraic groups over a finite field.

Flag manifolds are in general not symmetric spaces. But they are provided with a structure of $\mathbb{Z}_2^k$-symmetric space. We describe the Riemannian metrics adapted to this structure and some properties of reducibility. We detail for…

Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…

The main result of this article provides a characterization of reductive homogeneous spaces equipped with some geometric structure (non necessarily pseudo-Riemannian) in terms of the existence of certain connection. The result generalizes…

We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with…