scholarly journals Gravitational interaction of hadrons and leptons: Linear (multiplicity-free) bandor and nonlinear spinor unitary irreducible representations of SL(4R)

1979 ◽  
Vol 76 (2) ◽  
pp. 561-564 ◽  
Author(s):  
Y. Ne'eman ◽  
D. Sijacki
Keyword(s):  
Gravitational Interaction ◽  
Irreducible Representations ◽  
Nonlinear Spinor ◽  
Multiplicity Free

scholarly journals ON POSSIBLE GEOMETRIC AND ASTROPHYSICAL EFFECTS OF NONLINEAR SPINOR FIELDS IN THE MEGAMIR, MACROWORLD AND MICROWORLD

Metaphysics ◽  
2020 ◽  
pp. 82-93
Author(s):  
V. G Krechet
Keyword(s):  
General Relativity ◽  
Gravitational Interaction ◽  
Space Time ◽  
Elementary Particles ◽  
Nonlinear Spinor ◽  
Evolution Of The Universe ◽  
Spinor Fields ◽  
Astrophysical Objects ◽  
Local Space ◽  
The Universe

In this article, within the framework of general relativity, the possible effect of the gravitational interaction of Dirac nonlinear spinor fields on the evolution of the Universe, on the formation of astrophysical objects and on the formation of the geometry of the local space-time of elementary particles with spin ħ / 2 is considered.

scholarly journals THE SCHWINGER REPRESENTATION OF A GROUP: CONCEPT AND APPLICATIONS

2006 ◽  
Vol 18 (08) ◽  
pp. 887-912 ◽  
Author(s):  
S. CHATURVEDI ◽  
G. MARMO ◽  
N. MUKUNDA ◽  
R. SIMON ◽  
A. ZAMPINI
Keyword(s):  
Quantum Mechanics ◽  
Lie Group ◽  
Irreducible Representations ◽  
Quantum Mechanical ◽  
Direct Sum ◽  
Pure States ◽  
Group Concept ◽  
Set Up ◽  
Multiplicity Free

The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the Schwinger oscillator construction for SU(2), and its relevance in several quantum mechanical contexts is highlighted. The Schwinger representations for SU(2), SO(3) and SU(n) for all n are constructed via specific carrier spaces and group actions. In the SU(2) case, connections to the oscillator construction and to Majorana's theorem on pure states for any spin are worked out. The role of the Schwinger Representation in setting up the Wigner–Weyl isomorphism for quantum mechanics on a compact simple Lie group is brought out.

Some U(d1 + d2) ⊃ U(d1) ⊗ U(d2) isoscalar factors involving two-rowed initial and final representations

2019 ◽  
Vol 28 (08) ◽  
pp. 1950071
Author(s):  
H. G. Ganev
Keyword(s):  
Irreducible Representations ◽  
Type Formula ◽  
The One ◽  
Multiplicity Free

The elementary (one-particle) [Formula: see text] isoscalar factors, involving two-rowed initial and final irreducible representations (irreps), are obtained. Using the latter, further some of the multiplicity-free [Formula: see text] isoscalar factors, involving the [Formula: see text] couplings of the type [Formula: see text], are obtained using the building-up procedure. The present results extend the ones obtained earlier for the one-rowed initial and final irreps.

scholarly journals A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra

2021 ◽  
Vol 32 (1) ◽  
pp. 9-32
Author(s):  
C. Choi ◽  
◽  
S. Kim ◽  
H. Seo ◽  
◽  
...  
Keyword(s):  
Lie Algebra ◽  
Irreducible Representations ◽  
General Linear ◽  
Laurent Polynomials ◽  
Associated Graded Ring ◽  
Graded Ring ◽  
Weight Multiplicity ◽  
Direct Sum ◽  
Direct Sum Decomposition ◽  
Multiplicity Free

We first present a filtration on the ring Ln of Laurent polynomials such that the direct sum decomposition of its associated graded ring grLn agrees with the direct sum decomposition of grLn, as a module over the complex general linear Lie algebra gl(n), into its simple submodules. Next, generalizing the simple modules occurring in the associated graded ring grLn, we give some explicit constructions of weight multiplicity-free irreducible representations of gl(n).

scholarly journals Jucys–Murphy elements of partition algebras for the rook monoid

2021 ◽  
pp. 1-34
Author(s):  
Ashish Mishra ◽  
Shraddha Srivastava
Keyword(s):  
Representation Theory ◽  
Irreducible Representations ◽  
Spectral Approach ◽  
Inductive Approach ◽  
Partition Algebra ◽  
Rook Monoid ◽  
Partition Algebras ◽  
Weyl Duality ◽  
Multiplicity Free

Kudryavtseva and Mazorchuk exhibited Schur–Weyl duality between the rook monoid algebra [Formula: see text] and the subalgebra [Formula: see text] of the partition algebra [Formula: see text] acting on [Formula: see text]. In this paper, we consider a subalgebra [Formula: see text] of [Formula: see text] such that there is Schur–Weyl duality between the actions of [Formula: see text] and [Formula: see text] on [Formula: see text]. This paper studies the representation theory of partition algebras [Formula: see text] and [Formula: see text] for rook monoids inductively by considering the multiplicity free tower [Formula: see text] Furthermore, this inductive approach is established as a spectral approach by describing the Jucys–Murphy elements and their actions on the canonical Gelfand–Tsetlin bases, determined by the aforementioned multiplicity free tower, of irreducible representations of [Formula: see text] and [Formula: see text]. Also, we describe the Jucys–Murphy elements of [Formula: see text] which play a central role in the demonstration of the actions of Jucys–Murphy elements of [Formula: see text] and [Formula: see text].

scholarly journals Multiplicity Free Jacquet Modules

2012 ◽  
Vol 55 (4) ◽  
pp. 673-688 ◽  
Author(s):  
Avraham Aizenbud ◽  
Dmitry Gourevitch
Keyword(s):  
Finite Field ◽  
Natural Number ◽  
Parabolic Subgroup ◽  
Local Field ◽  
Classical Method ◽  
Irreducible Representations ◽  
Levi Subgroup ◽  
Unipotent Subgroup ◽  
Multiplicity Free

AbstractLet F be a non-Archimedean local field or a finite field. Let n be a natural number and k be 1 or 2. Consider G := GLn+k(F) and let M := GLn(F) × GLk(F) < G be a maximal Levi subgroup. Let U < G be the corresponding unipotent subgroup and let P = MU be the corresponding parabolic subgroup. Let be the Jacquet functor, i.e., the functor of coinvariants with respect toU. In this paper we prove that J is a multiplicity free functor, i.e., dim HomM(J(π), ρ) ≤ 1, for any irreducible representations π of G and ρ of M. We adapt the classical method of Gelfand and Kazhdan, which proves the “multiplicity free” property of certain representations to prove the “multiplicity free” property of certain functors. At the end we discuss whether other Jacquet functors are multiplicity free.

scholarly journals CENTRAL SEQUENCES IN SUBHOMOGENEOUS UNITAL C*-ALGEBRAS

2020 ◽  
pp. 1-8
Author(s):  
DON HADWIN ◽  
HEMANT PENDHARKAR
Keyword(s):  
Irreducible Representations ◽  
C Algebra ◽  
Central Sequence ◽  
C Algebras ◽  
Pointwise Limit ◽  
Central Sequences ◽  
Multiplicity Free

Abstract Suppose that $\mathcal {A}$ is a unital subhomogeneous C*-algebra. We show that every central sequence in $\mathcal {A}$ is hypercentral if and only if every pointwise limit of a sequence of irreducible representations is multiplicity free. We also show that every central sequence in $\mathcal {A}$ is trivial if and only if every pointwise limit of irreducible representations is irreducible. Finally, we give a nice representation of the latter algebras.

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