Related papers: Word maps in Kac-Moody setting
We describe a part of the recent developments in the theory of separately holomorphic mappings between complex analytic spaces. Our description focuses on works using the technique of holomorphic discs.
We study word maps with constants on symmetric groups. Even though there are mixed identities of bounded length that are valid for all symmetric groups, we show that no such identities hold in a metric sense. Moreover, we prove that word…
Lie algebra involutions and their fixed-point subalgebras give rise to symmetric spaces and real forms of complex Lie algebras, and are well-studied in the context of symmetrizable Kac-Moody algebras. In this paper we study a…
We show that a canonical procedure of extending generalized Dynkin diagrams gives rise to families of Kac-Moody groups that satisfy homological stability. We also briefly sketch some emergent structure that appears on stabilization. Our…
The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.
In this paper, we study a special class of indefinite Kac-Moody algebras. Based on the study of hyperbolic Kac-Moody algebras, we give the definition of $N_k$ type Kac-Moody algebras and study some properties of this special type Kac-Moody…
The goal of the present paper is to obtain new free field realizations of affine Kac-Moody algebras motivated by geometric representation theory for generalized flag manifolds of finite-dimensional semisimple Lie groups. We provide an…
This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.
Riemannian symmetric spaces are fundamental objects in finite dimensional differential geometry. An important problem is the construction of symmetric spaces for generalizations of simple Lie groups, especially their closest infinite…
We present a new framework for dealing with $C^{\infty}$-words, based on their left and right frontiers. This allows us to give a compact representation of them, and to describe the set of $C^{\infty}$-words through an infinite directed…
This short survey contains some recent developments of the algebraic theory of racks and quandles. We report on some elements of representation theory of quandles and ring theoretic approach to quandles.
Given a projective variety X and a smooth projective curve C one may consider the moduli space of maps C --> X. This space admits certain compactification whose points are called quasi-maps. In the last decade it has been discovered that in…
This is the second of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps. It contains two parts: (1) the…
The dual space of the Cartan subalgebra in a Kac-Moody algebra has a partial ordering defined by the rule that two elements are related if and only if their difference is a non-negative or non-positive integer linear combination of simple…
The purpose of this paper is to present a systematic exposition of the main results obtained in the studies carried out in groupoid theory. Key words and phrases: groupoid, topological groupoid, Lie groupoid, group-groupoid, vector…
We provide a further analysis of the class of positive maps proposed ten years ago by Kossakowski. In particular we propose a new parametrization which reveals an elegant geometric structure and an interesting interplay between group theory…
In this article we investigate rigidity properties of $S$-arithmetic Kac-Moody groups in characteristic $0$.
In previous work a relation between a large class of Kac-Moody algebras and meromorphic connections on global curves was established---notably the Weyl group gives isomorphisms between different moduli spaces of connections, and the root…
The theory of standard pentads is the theory aims to construct a graded Lie algebra whose local part consists of a given Lie algebra and its representation. In other words, using standard pentads, we can embed given Lie algebra and its…
Weyl groups are ubiquitous, and efficient algorithms for them -- especially for the exceptional algebras -- are clearly desirable. In this paper we provide several of these, addressing practical concerns arising naturally for instance in…