By Jian-Shu Li, Eng-Chye Tan, Nolan R Wallach, Chen-Bo Zhu
This quantity consists of a similar name as that of a world convention held on the nationwide collage of Singapore, 11th of September January 2006 at the social gathering of Roger E. Howe's sixtieth birthday. Authored through major contributors of the Lie idea group, those contributions, elevated from invited lectures given on the convention, are a becoming tribute to the originality, intensity and effect of Howe's mathematical paintings. the diversity and variety of the subjects will entice a huge viewers of analysis mathematicians and graduate scholars drawn to symmetry and its profound functions.
By Madabusi S. Raghunathan
This ebook originated from a process lectures given at Yale college in the course of 1968-69 and a extra complex one, the following yr, on the Tata Institute of basic learn. Its goal is to provide an in depth ac count number of a few of the hot paintings at the geometric elements of the speculation of discrete subgroups of Lie teams. Our curiosity, generally, is in a distinct classification of discrete subgroups of Lie teams, viz., lattices (by a lattice in a in the neighborhood compact team G, we suggest a discrete subgroup H such that the homogeneous area GJ H contains a finite G-invariant measure). it's assumed that the reader has enormous familiarity with Lie teams and algebraic teams. besides the fact that lots of the effects used often within the e-book are summarised in "Preliminaries"; this bankruptcy, it really is was hoping, can be invaluable as a reference. We now in brief define the contents of the booklet. bankruptcy I offers with result of a basic nature on lattices in in the neighborhood compact teams. the second one bankruptcy is an account of the rather entire learn of lattices in nilpotent Lie teams conducted via Ma1cev. Chapters III and IV are dedicated to lattices in solvable Lie teams; lots of the theorems listed below are as a result of Mostow. In bankruptcy V we turn out a density theorem as a result of Borel: this is often the 1st vital outcome on lattices in semisimple Lie teams.
By Augustin Banyaga
In the 60's, the paintings of Anderson, Chernavski, Kirby and Edwards confirmed that the crowd of homeomorphisms of a delicate manifold that are isotopic to the id is a straightforward staff. This led Smale to conjecture that the gang Diff'" (M)o of cr diffeomorphisms, r ~ 1, of a soft manifold M, with compact helps, and isotopic to the id via compactly supported isotopies, is an easy staff besides. during this monograph, we supply a reasonably distinctive evidence that DifF(M)o is a straightforward staff. This theorem was once proved through Herman within the case M is the torus rn in 1971, because of the Nash-Moser-Sergeraert implicit functionality theorem. Thurston confirmed in 1974 how Herman's end result on rn implies the final theorem for any soft manifold M. the major suggestion was once to imaginative and prescient an isotopy in Diff'"(M) as a foliation on M x [0, 1]. in reality he found a deep connection among the neighborhood homology of the gang of diffeomorphisms and the homology of the Haefliger classifying house for foliations. Thurston's paper  comprises only a short comic strip of the facts. the main points were labored out by means of Mather , , , and the writer . This circle of principles that we name the "Thurston tips" is mentioned in bankruptcy 2. It explains how in yes teams of diffeomorphisms, perfectness ends up in simplicity. In reference to those rules, we talk about Epstein's concept , which we observe to touch diffeomorphisms in bankruptcy 6.
By Alexander Kleshchev
The illustration concept of symmetric teams is likely one of the most lovely, well known, and critical elements of algebra with many deep kinfolk to different parts of arithmetic, comparable to combinatorics, Lie concept, and algebraic geometry. Kleshchev describes a brand new method of the topic, in line with the hot paintings of Lascoux, Leclerc, Thibon, Ariki, Grojnowski, Brundan, and the writer. a lot of this paintings has simply seemed within the learn literature ahead of. despite the fact that, to make it available to graduate scholars, the speculation is constructed from scratch, the one prerequisite being a customary path in summary algebra. Branching principles are in-built from the outset leading to a proof and generalization of the hyperlink among modular branching ideas and crystal graphs for affine Kac-Moody algebras. The tools are in simple terms algebraic, exploiting affine and cyclotomic Hecke algebras. For the 1st time in publication shape, the projective (or spin) illustration idea is taken care of alongside a similar strains as linear illustration thought. the writer is especially involved in modular illustration conception, even if every little thing works in arbitrary attribute, and in case of attribute zero the process is a bit of just like the idea of Okounkov and Vershik, defined right here in bankruptcy 2. For the sake of transparency, Kleshschev concentrates on symmetric and spin-symmetric teams, even though the equipment he develops are really common and observe to a couple of similar items. In sum, this special e-book could be welcomed by way of graduate scholars and researchers as a contemporary account of the topic.