Related papers: A Product Theorem in simple Lie groups

We study properties of a family of algebraic star products defined on coadjoint orbits of semisimple Lie groups. We connect this description with the point of view of differentiable deformations and geometric quantization.

Groups with a large $p$-subgroup, $p$ a prime, include almost all of the groups of Lie type in characteristic $p$ and so the study of such groups adds to our understanding of the finite simple groups. In this article we study a special…

Solving non-autonomous systems of ordinary differential equations leads to consider a new product of bivariate distributions called the $\star$~product in the literature. This product, distinct from the convolution product, has recently…

It has recently been proved that the class of unital exact C*-algebras is closed under taking reduced amalgamated free products. In particular, this implied that the class of exact discrete groups is closed under taking amalgamated free…

We establish a tensor product theorem for slope semistable parabolic $\lambda$-connections over smooth projective varieties in arbitrary characteristic.

In an earlier paper, we gave an abstract formulation of a theorem of Sierpi\'nski in uncountable commutative groups. In this paper, we prove a result which generalizes the earlier formulation.

We provide a self-contained proof of the main properties of Brauer quotients of Young modules. We then use these results to give a new inductive proof of Nakayama's Conjecture on the blocks of the symmetric group.

We study the $\delta$-discretized sum-product estimates for well spaced sets. Our main result is: for a fixed $\alpha\in(1,\frac{3}{2}]$, we prove that for any $\sim|A|^{-1}$-separated set $A\subset[1,2]$ and $\delta=|A|^{-\alpha}$, we…

It is known that Plotkin's reduction theorem is very important for his theory of universal algebraic geometry [arXiv:math. GM/0210187], [arXiv:math. GM/0210194]. It turns out that this theorem can be generalized to arbitrary categories…

We introduce some deformations of the biset category and prove a semisimplicity property. We also consider another group category, called the subgroup category, whose morphisms are subgroups of direct products, the composition being star…

This paper presents the continuous and discrete variational formulations of simple thermodynamical systems whose configuration space is a (finite dimensional) Lie group. We follow the variational approach to nonequilibrium thermodynamics…

We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…

We consider the Lie algebra associated with the descending central series filtration of the pure braid group of a closed surface of arbitrary genus. R. Bezrukavnikov gave a presentation of this Lie algebra over the rational numbers. We show…

We prove that every quasisimple group of classical type is a product of boundedly many conjugates of a quasisimple subgroup of type A_n.

A simple application of the semipositivity.

We prove upper and lower bounds for certain sums of products of fractional parts by using majoring and minorizing functions from Fourier analysis. In special cases the upper bounds are sharp if there exist counterexamples to the Littlewood…

We extend Gow's theorem on products of semisimple regular conjugacy classes to finite groups whose generalized Fitting subgroup is Z(G)S where S is a quasisimple group of Lie type in characteristic p and Z(G) has order prime to p.

This note is devoted to the theory of projective limits of finite-dimensional Lie groups, as developed in the recent monograph ``The Lie Theory of Connected Pro-Lie Groups'' by K.H. Hofmann and S.A. Morris. We replace the original, highly…

The Recognition Theorem for graded Lie algebras is an essential ingredient in the classification of finite-dimensional simple Lie algebras over an algebraically closed field of characteristic p > 3. The main goal of this monograph is to…

We generalize Bourgain's discretized projection theorem to higher rank situations. Like Bourgain's theorem, our result yields an estimate for the Hausdorff dimension of the exceptional sets in projection theorems formulated in terms of…