相关论文: Connected components of real double Bruhat cells

In math.SG/0303255, we discussed the connected components of the space of surface group representations for any compact connected semisimple Lie group and any closed compact (orientable or nonorientable) surface. In this sequel, we…

We study the intersection of the totally positive part of a split semisimple group over the real numbers with a totally positive parabolic subgroup.

We conclude our analysis of bubble divergences in the flat spinfoam model. In [arXiv:1008.1476] we showed that the divergence degree of an arbitrary two-complex Gamma can be evaluated exactly by means of twisted cohomology. Here, we…

In this paper, we study half-densities enhancing the multiplication map on a symplectic groupoid and which satisfy a suitable associativity condition. This is structurally motivated by the expected complete semiclassical-analytic…

The complement of a complex hyperplane arrangement is known to be homotopic to a minimal CW complex. There are several approaches to the minimality. In this paper, we restrict our attention to real two dimensional cases, and introduce the…

In this note we construct a poset map from a Boolean algebra to the Bruhat order which unveils an interesting connection between subword complexes, sorting orders, and certain totally nonnegative spaces. This relationship gives a new proof…

Double Bruhat cells $G^{u,v}$ were studied by Fomin and Zelevinsky. They provide important examples of cluster algebras and cluster Poisson varieties. Cluster varieties produce examples of 3d Calabi-Yau categories with stability conditions,…

For a connected semisimple Lie group $G$ we describe an explicit collection of correspondences between the admissible dual of $G$ and the admissible dual of the Cartan motion group associated with $G$. We conjecture that each of these…

Starting from a split semisimple real Lie group G with trivial center, we define a family of varieties with additional structures. We describe them as the cluster X-varieties, as defined in math.AG/0311245. In particular they are Poisson…

Let $G$ denote an adjoint semi-simple group over an algebraically closed field and $T$ a maximal torus of $G$. Following Contou-Carr\`ere [CC], we consider the Bott-Samelson resolution of a Schubert variety as a variety of galleries in the…

In this note the notion of Poisson brackets in Kontsevich's "Lie World" is developed. These brackets can be thought of as "universally" defined classical Poisson structures, namely formal expressions only involving the structure maps of a…

As an example of the categorical apparatus of pseudo algebras over 2-theories, we show that pseudo algebras over the 2-theory of categories can be viewed as pseudo double categories with folding or as appropriate 2-functors into…

Using the relations between the theory of differentiable Bol loops and the theory of affine symmetric spaces we classify all connected differentiable Bol loops having an at most $9$-dimensional semi-simple Lie group as the group…

This article describes a natural piecewise Euclidean bi-simplicial cell structure for the space of $n$-element multisets in a fixed Euclidean rectangle. In particular, we highlight some connections with spaces of complex polynomials and…

The construction of Lie bialgebra from double Lie algebra is presented. It is used to relate some types of cobracket on inhomogenous so(p,q) algebras with double Lie algebra structures on so(p+1,q) or so(p,q+1). Also it is shown that the…

Let $G$ be any connected and simply connected complex semisimple Lie group, equipped with a standard holomorphic multiplicative Poisson structure. We show that the Hamiltonian flows of all the Fomin-Zelevinsky twisted generalized minors on…

We construct a compactification of the Bruhat-Tits building associated to the group PGL(V) which can be identified with the space of homothety classes of seminorms on V endowed with the topology of pointwise convergence. Then we define a…

Motivated by the Bruhat and Cartan decompositions of general linear groups over local fields, double cosets of the group of label preserving automorphisms of a label-regular tree over the fixator of an end of the tree and over maximal…

We introduce Poisson double algebroids, and the equivalent concept of double Lie bialgebroid, which arise as second-order infinitesimal counterparts of Poisson double groupoids. We develop their underlying Lie theory, showing how these…

We suggest two explicit descriptions of the Poisson q-W algebras which are Poisson algebras of regular functions on certain algebraic group analogues of the Slodowy transversal slices to adjoint orbits in a complex semisimple Lie algebra g.…