G-Majorization, group-induced cone orderings, and reflection groups
نویسندگان
چکیده
منابع مشابه
Imaginary Cone and Reflection Subgroups of Coxeter Groups
The imaginary cone of a Kac-Moody Lie algebra is the convex hull of zero and the positive imaginary roots. This paper studies the imaginary cone for a class of root systems of general Coxeter groups W . It is shown that the imaginary cone of a reflection subgroup of W is contained in that of W , and that for irreducible infinite W of finite rank, the closed imaginary cone is the only non-zero, ...
متن کاملDiscrete Reflection Groups and Induced Representations of Poincare Group on the Lattice
We continue the program, presented in previous Symposia, of discretizing physical models. In particular we calculate the integral Lorentz transformations with the help of discrete reflection groups, and use them for the covariance of Klein-Gordon and Dirac wave equation on the lattice. Finally we define the unitary representation of Poincaré group on discrete momentum and configuration space, i...
متن کاملLinear preservers of g-row and g-column majorization on M_{n,m}
Let A and B be n × m matrices. The matrix B is said to be g-row majorized (respectively g-column majorized) by A, if every row (respectively column) of B, is g-majorized by the corresponding row (respectively column) of A. In this paper all kinds of g-majorization are studied on Mn,m, and the possible structure of their linear preservers will be found. Also all linear operators T : Mn,m ---> Mn...
متن کاملREFLECTION ORDERING ON THE GROUP G ( m , m , n )
In the paper [13], we introduced a partial ordering, called the reflection ordering, on the elements of G(m, p, n) and described such an ordering on the groups G(m, 1, n), m > 1. In the present paper, we describe the reflection ordering on the group G(m,m,n). As a by-product, we obtain a formula for the enumeration of a certain subset in the symmetric group Sn, which is of independent combinato...
متن کاملPalindromes and Orderings in Artin Groups
The braid group Bn, endowed with Artin’s presentation, admits two distinguished involutions. One is the anti-automorphism rev : Bn → Bn, v 7→ v̄, defined by reading braids in the reverse order (from right to left instead of left to right). Another one is the conjugation τ : x 7→ ∆x∆ by the generalized half-twist (Garside element). More generally, the involution rev is defined for all Artin group...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1990
ISSN: 0024-3795
DOI: 10.1016/0024-3795(90)90338-d