Minimal faces and Schur's Lemma for embeddings into $R^\mathcal{U}$

2018 ◽  
Vol 67 (4) ◽  
pp. 1327-1340
Author(s):  
Scott Atkinson
Keyword(s):  
Schur’S Lemma ◽  
Schur's Lemma

scholarly journals A Remark on the Orthogonality Relations in the Representation Theory of Finite Groups

1959 ◽  
Vol 11 ◽  
pp. 59-60 ◽  
Author(s):  
Hirosi Nagao
Keyword(s):  
Finite Group ◽  
Irreducible Representation ◽  
Representation Theory ◽  
Finite Groups ◽  
Characteristic Zero ◽  
Orthogonality Relations ◽  
Schur’S Lemma ◽  
Image Position ◽  
A Finite Group ◽  
Schur's Lemma

Let G be a finite group of order g, andbe an absolutely irreducible representation of degree fμ over a field of characteristic zero. As is well known, by using Schur's lemma (1), we can prove the following orthogonality relations for the coefficients :1It is easy to conclude from (1) the following orthogonality relations for characters:whereand is 1 or 0 according as t and s are conjugate in G or not, and n(t) is the order of the normalize of t.

scholarly journals Family Symmetries and Multi Higgs Doublet Models

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 156
Author(s):  
Bartosz Dziewit ◽  
Jacek Holeczek ◽  
Sebastian Zając ◽  
Marek Zrałek
Keyword(s):  
Standard Model ◽  
Higgs Doublet ◽  
Family Symmetry ◽  
The Standard Model ◽  
Schur’S Lemma ◽  
Finite Subgroups ◽  
Free Parameters ◽  
Schur's Lemma

Imposing a family symmetry on the Standard Model in order to reduce the number of its free parameters, due to the Schur’s Lemma, requires an explicit breaking of this symmetry. To avoid the need for this symmetry to break, additional Higgs doublets can be introduced. In such an extension of the Standard Model, we investigate family symmetries of the Yukawa Lagrangian. We find that adding a second Higgs doublet (2HDM) does not help, at least for finite subgroups of the U ( 3 ) group up to the order of 1025.

Schur’s lemma for Kähler manifolds

2008 ◽  
Vol 90 (2) ◽  
pp. 163-172
Author(s):  
Toshiaki Adachi ◽  
Sadahiro Maeda ◽  
Seiichi Udagawa
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Schur’S Lemma ◽  
Schur's Lemma

Decomposition of group rings and the converse of Schur’s lemma

2017 ◽  
Vol 46 (2) ◽  
pp. 664-670 ◽  
Author(s):  
Mostafa Alaoui Abdallaoui ◽  
Mohammed El Badry ◽  
Abdelfattah Haily
Keyword(s):  
Group Rings ◽  
Schur’S Lemma ◽  
Schur's Lemma

On Generalized Schur's Lemma and Its Applications

2012 ◽  
Vol 19 (02) ◽  
pp. 337-352 ◽  
Author(s):  
Lizhong Wang
Keyword(s):  
Representation Theory ◽  
Endomorphism Ring ◽  
Symmetric Groups ◽  
Modular Representation ◽  
Modular Representation Theory ◽  
Endomorphism Rings ◽  
Natural Embedding ◽  
Induced Module ◽  
Schur’S Lemma ◽  
Schur's Lemma

In this paper, we generalize Schur's lemma on the basis of endomorphism rings for permutation modules. Let H be a subgroup of G and let M be a module of H. Set N = NG(H). Then there is a natural embedding of End N(MN) into End G(MG). By taking H to be a p-subgroup of G, we can reformulate Green's theory on modular representation. A defect theory is defined on the endomorphism ring of any induced module and it is used to prove Green's correspondence and related results. This defect theory can unify some well known results in modular representation theory. By using generalized Schur's lemma, we can also give a method to determine the multiplicity of simple modules in any permutation module of symmetric groups. This makes it possible to prove various versions of Foulkes' conjecture in a uniform way.

Sign in / Sign up

Export Citation Format

Share Document