Topic
General linear group
About: General linear group is a research topic. Over the lifetime, 1571 publications have been published within this topic receiving 20373 citations. The topic is also known as: GL(n).
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this paper, it was shown that, in space-times which are asymptotically flat, there are reasonable physical restrictionsthat allow one to impose coordinate conditions (in addition to the usual Bondi-type conditions) which restrict the allowed coordinate group to a subgroup of the Bondi Metzner-Sachsgroup.
Abstract: It is shown that, in space-times which are asymptotically flat, there are reasonable physical restrictionsthat allow one to impose coordinate conditions (in addition to the usual Bondi-type conditions)which restrict the allowed coordinate group to a subgroup of the Bondi-Metzner-Sachsgroup. This subgroup is isomorphic to the improper orthochronous inhomogeneous Lorentz group.
900 citations
Book•
1 Jan 1993
TL;DR: In this paper, the authors define a family of representations of these compact open subgroups, which they call "simple types" and classify the irreducible representations of "G" containing the trivial simple type by the simple modules over a classical affine Hecke algebra.
Abstract: This work gives a full description of a method for analyzing the admissible complex representations of the general linear group "G" = "Gl(N, F)" of a non-Archimedean local field "F" in terms of the structure of these representations when they are restricted to certain compact open subgroups of "G." The authors define a family of representations of these compact open subgroups, which they call "simple types." The first example of a simple type, the "trivial type," is the trivial character of an Iwahori subgroup of "G." The irreducible representations of "G" containing the trivial simple type are classified by the simple modules over a classical affine Hecke algebra. Via an isomorphism of Hecke algebras, this classification is transferred to the irreducible representations of "G" containing a given simple type. This leads to a complete classification of the irreduc-ible smooth representations of "G," including an explicit description of the supercuspidal representations as induced representations. A special feature of this work is its virtually complete reliance on algebraic methods of a ring-theoretic kind. A full and accessible account of these methods is given here.
504 citations
TL;DR: In this article, it was shown that the special linear group of degree not less than three over the polynomial ring over a field is generated by the elementary matrices, and that the general linear group over the Laurent ring is also composed of the same matrices.
Abstract: It is proved that the special linear group of degree not less than three over the polynomial ring over a field is generated by the elementary matrices. Other results are obtained that relate to the structure of the special linear group and stabilization of the general linear group over arbitrary polynomial and Laurent rings.Bibliography: 9 titles.
422 citations
Book•
1 Jan 1971TL;DR: In this article, the authors present a general linear group representation of the General Linear Group (GL(n, Q) and show that the characters of GL(n; Q) are invariants of antisymmetric tensors.
Abstract: Chapter 2. Rational Representations of the General Linear Group ... 10 1. Representations of Linear Groups 10 2. Representations of the Full Linear Group 14 3. Young’s Diagrams 16 4. The Characters of GL (n; 9) 20 5. Multilinear Invariants of GL (n; Q) 22 6. Invariants of Antisymmetric Tensors 26 7. Invariants of Mixed Tensors 28 8. Gram’s Theorem 31 9. Invariants of n-ary Forms: The Symbolic Method ...... 32 10. Invariants of subgroups of GL (n; Q) 37
285 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 5 |
| 2024 | 6 |
| 2023 | 13 |
| 2022 | 31 |
| 2021 | 63 |
| 2020 | 79 |