Groups of Galaxies.IV. The Multiplicity Function

1977 ◽  
Vol 216 ◽  
pp. 357 ◽  
Author(s):  
J. Richard, III Gott ◽  
Edwin L. Turner
Keyword(s):  
Multiplicity Function

scholarly journals GROUP ACTIONS AND COVERINGS OF BRAUER GRAPH ALGEBRAS

2013 ◽  
Vol 56 (2) ◽  
pp. 439-464 ◽  
Author(s):  
EDWARD L. GREEN ◽  
SIBYLLE SCHROLL ◽  
NICOLE SNASHALL
Keyword(s):  
Group Actions ◽  
Multiplicity Function ◽  
Graph Algebras ◽  
Multiple Edges

AbstractWe develop a theory of group actions and coverings on Brauer graphs that parallels the theory of group actions and coverings of algebras. In particular, we show that any Brauer graph can be covered by a tower of coverings of Brauer graphs such that the topmost covering has multiplicity function identically one, no loops, and no multiple edges. Furthermore, we classify the coverings of Brauer graph algebras that are again Brauer graph algebras.

On the multiplicity function of generic group extensions with continuous spectrum

2001 ◽  
Vol 21 (2) ◽  
pp. 321-338 ◽  
Author(s):  
OLEG N. AGEEV
Keyword(s):  
Continuous Spectrum ◽  
Lebesgue Space ◽  
Unitary Operator ◽  
Multiplicity Function ◽  
Group Extensions ◽  
Geometric Models ◽  
Generic Group ◽  
Weakly Mixing ◽  
Generic Set

A modification of the method of geometric models is proposed and applied to the study of multiplicity functions of group extensions.It is proved that, for some generic set of the automorphisms T of the Lebesgue space with respect to the standard topology, for any M\subseteq {\mathbb N} \cup \{\infty\}(1\in M) there exists a generic set of weakly mixing group extensions T' of transformation T with M(T')=M, where M(T) denotes the set of essential spectral multiplicities of the unitary operator corresponding to the transformation T.

scholarly journals Merger trees and the multiplicity function of haloes

1996 ◽  
Vol 282 (2) ◽  
pp. 631-640 ◽  
Author(s):  
D. D. C. Rodrigues ◽  
P. A. Thomas
Keyword(s):  
Multiplicity Function

scholarly journals Boundary value problems for the Dunkl Laplacian

2018 ◽  
Vol 38 (2) ◽  
pp. 249-269
Author(s):  
Mohamed Ben Chrouda ◽  
Khalifa El Mabrouk ◽  
Kods Hassine
Keyword(s):  
Unit Ball ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Boundary Value ◽  
Reflection Group ◽  
Multiplicity Function ◽  
Dunkl Laplacian

Let Δk be the Dunkl Laplacian on ℜd associated with a reflection group W and a multiplicity function k. The purpose of this paper is to establish the existence and the uniqueness of a positive solution on the unit ball B of ℜd to the following boundary value problem:Δku = φu in B and u = ƒ on ∂BWe distinguish two cases of nonnegative perturbation φ: trivial and nontrivial.   

scholarly journals The multiplicity function of galaxies

2003 ◽  
Vol 403 (1) ◽  
pp. 73-81 ◽  
Author(s):  
E. Puddu ◽  
E. De Filippis ◽  
G. Longo ◽  
S. Andreon ◽  
R. R. Gal
Keyword(s):  
Multiplicity Function

scholarly journals Corwin–Greenleaf multiplicity function for compact extensions of the Heisenberg group

2018 ◽  
Vol 29 (09) ◽  
pp. 1850056
Author(s):  
Majdi Ben Halima ◽  
Anis Messaoud
Keyword(s):  
Heisenberg Group ◽  
Lie Algebras ◽  
Closed Subgroup ◽  
Sufficient Conditions ◽  
Multiplicity Function ◽  
Coadjoint Orbits ◽  
Gelfand Pair ◽  
Irreducible Unitary Representations ◽  
Multiplicity Formula ◽  
The Relationship

Let [Formula: see text] be the [Formula: see text]-dimensional Heisenberg group and [Formula: see text] a closed subgroup of [Formula: see text] acting on [Formula: see text] by automorphisms such that [Formula: see text] is a Gelfand pair. Let [Formula: see text] be the semidirect product of [Formula: see text] and [Formula: see text]. Let [Formula: see text] be the respective Lie algebras of [Formula: see text] and [Formula: see text], and [Formula: see text] the natural projection. For coadjoint orbits [Formula: see text] and [Formula: see text], we denote by [Formula: see text] the number of [Formula: see text]-orbits in [Formula: see text], which is called the Corwin–Greenleaf multiplicity function. In this paper, we give two sufficient conditions on [Formula: see text] in order that [Formula: see text] For [Formula: see text], assuming furthermore that [Formula: see text] and [Formula: see text] are admissible and denoting respectively by [Formula: see text] and [Formula: see text] their corresponding irreducible unitary representations, we also discuss the relationship between [Formula: see text] and the multiplicity [Formula: see text] of [Formula: see text] in the restriction of [Formula: see text] to [Formula: see text]. Especially, we study in Theorem 4 the case where [Formula: see text]. This inequality is interesting because we expect the equality as the naming of the Corwin–Greenleaf multiplicity function suggests.

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