A ug 2 00 2 QUASIDETERMINANTS

O ct 2 00 3 Quasideterminants and Casimir elements for the general linear Lie superalgebra

We apply the techniques of quasideterminants to construct new families of Casimir elements for the general linear Lie superalgebra gl(m|n) whose images under the Harish-Chandra isomorphism are respectively the elementary, complete and power sums supersymmetric functions. School of Mathematics and Statistics University of Sydney, NSW 2006, Australia [email protected] Department of Mathemat...

ar X iv : m at h / 98 08 06 5 v 1 [ m at h . Q A ] 1 4 A ug 1 99 8 QUANTUM DETERMINANTS AND QUASIDETERMINANTS

A ug 2 00 4 A substantial amount of hidden magnetic energy in the quiet Sun

X iv :a st ro -p h/ 04 09 00 4v 1 3 1 A ug 2 00 4 A substantial amount of hidden magnetic energy in the quiet Sun J. Trujillo Bueno, N. Shchukina & A. Asensio Ramos ∗ Instituto de Astrof́ısica de Canarias, E-38205 La Laguna, Tenerife, Spain. + Main Astronomical Observatory, National Academy of Sciences, Zabolotnogo 27, 03680 Kyiv, Ukraine † Consejo Superior de Investigaciones Cient́ıficas, E-2800...

ar X iv : h ep - e x / 00 08 06 5 v 1 2 6 A ug 2 00 0 Search for Large Extra Dimensions in Dielectron and Diphoton Production

Noncommutative Double Bruhat Cells and Their Factorizations

0. Introduction 1 1. Quasideterminants and Quasiminors 3 1.1. Definition of quasideterminants 3 1.2. Elementary properties of quasideterminants 4 1.3. Noncommutative Sylvester formula 5 1.4. Quasi-Plücker coordinates and Gauss LDU -factorization 5 1.5. Positive quasiminors 6 2. Basic factorizations in GLn(F) 7 3. Examples 11 3.1. A factorization in the Borel subgroup of GL3(F) 11 3.2. A factori...