scholarly journals For Coxeter groups z|g|is a coefficient of a uniformly bounded representation

2002 ◽  
Vol 174 (1) ◽  
pp. 79-86 ◽  
Author(s):  
Tadeusz Januszkiewicz
Keyword(s):  
Coxeter Groups ◽  
Bounded Representation ◽  
Uniformly Bounded

Simple motion systems and Banach spaces associated to uniformly bounded representations

1999 ◽  
Vol 127 (1) ◽  
pp. 133-147
Author(s):  
MATTHIAS MAYER ◽  
CHRISTIAN SALLER
Keyword(s):  
Convex Hull ◽  
Locally Compact Group ◽  
Irreducible Representations ◽  
Minkowski Functional ◽  
Linear Hull ◽  
Locally Compact ◽  
Simple Motion ◽  
Motion System ◽  
Bounded Representation ◽  
Uniformly Bounded

Given a uniformly bounded representation of a locally compact group, we consider the closed circled convex hull K of the orbit of a vector. We call K a simple motion system (SMS) and endow its linear hull with the Minkowski functional of K. The representation theory on these ‘SMS-spaces’ is discussed, in particular for C0-representations, for irreducible representations of connected groups and for integrable representations. As an application we give a criterion for the decomposibility of representations.

scholarly journals Automorphisms of odd Coxeter groups

2021 ◽  
Author(s):  
Tushar Kanta Naik ◽  
Mahender Singh
Keyword(s):  
Coxeter Groups

scholarly journals The 300 “correlators” suggests 4D, $$ \mathcal{N} $$ = 1 SUSY is a solution to a set of Sudoku puzzles

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Aleksander J. Cianciara ◽  
S. James Gates ◽  
Yangrui Hu ◽  
Renée Kirk
Keyword(s):  
Coxeter Groups ◽  
Auxiliary Field ◽  
Permutation Groups ◽  
Weight Space ◽  
Field Problem ◽  
Truncated Octahedron ◽  
Color Problem ◽  
Minimal Representations

Abstract A conjecture is made that the weight space for 4D, $$ \mathcal{N} $$ N -extended supersymmetrical representations is embedded within the permutahedra associated with permutation groups 𝕊d. Adinkras and Coxeter Groups associated with minimal representations of 4D, $$ \mathcal{N} $$ N = 1 supersymmetry provide evidence supporting this conjecture. It is shown that the appearance of the mathematics of 4D, $$ \mathcal{N} $$ N = 1 minimal off-shell supersymmetry representations is equivalent to solving a four color problem on the truncated octahedron. This observation suggest an entirely new way to approach the off-shell SUSY auxiliary field problem based on IT algorithms probing the properties of 𝕊d.

scholarly journals Some Conditions under Which Sequences of Functions are Uniformly Bounded

1968 ◽  
Vol 33 ◽  
pp. 75-83
Author(s):  
D.C. Rung
Keyword(s):  
Complex Analysis ◽  
Normal Family ◽  
Normal Families ◽  
Usual Pattern ◽  
Uniformly Bounded

After one introduces the theory of normal families in a course in complex analysis, the usual pattern is to give an example of a non-normal family. One of the simplest, of course, is the sequence fn(z) = nz, n = 1,2, ···. The very devastating effect of multiplying by zero insures the required abnormality!

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