Symmetry breaking operators for the restriction of representations of indefinite orthogonal groups $O(p,q)$

AbstractLet G be a group and let H be a subgroup of G. The classical branching rule (or symmetry breaking) asks: For an irreducible representation π of G, determine the occurrence of an irreducible representation σ of H in the restriction of π to H. The reciprocal branching problem of this classical branching problem is to ask: For an irreducible representation σ of H, find an irreducible representation π of G such that σ occurs in the restriction of π to H. For automorphic representations of classical groups, the branching problem has been addressed by the well-known global Gan–Gross–Prasad conjecture. In this paper, we investigate the reciprocal branching problem for automorphic representations of special orthogonal groups using the twisted automorphic descent method as developed in [13]. The method may be applied to other classical groups as well.

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Symmetry Breaking Patterns for Unitary and Orthogonal Groups

First Workshop on Grand Unification ◽

10.1007/978-1-4684-6903-5_4 ◽

1980 ◽

pp. 23-32

Author(s):

H. Ruegg

Keyword(s):

Symmetry Breaking ◽

Orthogonal Groups

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ON THE ISOMORPHIC DESCRIPTION OF CHIRAL SYMMETRY BREAKING BY NONUNITARY LIE GROUPS

International Journal of Modern Physics A ◽

10.1142/s0217751x10048123 ◽

2010 ◽

Vol 25 (08) ◽

pp. 1699-1712 ◽

Cited By ~ 2

Author(s):

WOLFGANG BIETENHOLZ

Keyword(s):

Symmetry Breaking ◽

Lie Groups ◽

Chiral Symmetry ◽

Chiral Symmetry Breaking ◽

Light Quark ◽

Higgs Mechanism ◽

Orthogonal Groups ◽

Mass Generation ◽

Trace Back ◽

Exceptional Lie Groups

It is well known that chiral symmetry breaking (χSB) in QCD with Nf = 2 light quark flavors can be described by orthogonal groups as O (4) → O (3), due to local isomorphisms. Here we discuss the question how specific this property is. We consider generalized forms of χSB involving an arbitrary number of light flavors of continuum or lattice fermions, in various representations. We search systematically for isomorphic descriptions by nonunitary, compact Lie groups. It turns out that there are a few alternative options in terms of orthogonal groups, while we did not find any description entirely based on symplectic or exceptional Lie groups. If we adapt such an alternative as the symmetry breaking pattern for a generalized Higgs mechanism, we may consider a Higgs particle composed of bound fermions and trace back the mass generation to χSB. In fact, some of the patterns that we encounter appear in technicolor models. In particular if one observes a Higgs mechanism that can be expressed in terms of orthogonal groups, we specify in which cases it could also represent some kind of χSB of techniquarks.

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Symmetry Breaking for Orthogonal Groups and a Conjecture by B. Gross and D. Prasad

Simons Symposia - Geometric Aspects of the Trace Formula ◽

10.1007/978-3-319-94833-1_8 ◽

2018 ◽

pp. 245-266

Author(s):

Toshiyuki Kobayashi ◽

Birgit Speh

Keyword(s):

Symmetry Breaking ◽

Orthogonal Groups

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Symmetry breaking in convergent-beam diffraction

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100154378 ◽

1989 ◽

Vol 47 ◽

pp. 480-481

Author(s):

D.J. Eaglesham

Keyword(s):

Symmetry Breaking ◽

Point Group ◽

X Ray Diffraction ◽

Multiple Diffraction ◽

Space Groups ◽

Atomic Displacements ◽

Small Probe ◽

Phase Sensitive ◽

Convergent Beam

Convergent Beam Electron Diffraction is now almost routinely used in the determination of the point- and space-groups of crystalline samples. In addition to its small-probe capability, CBED is also postulated to be more sensitive than X-ray diffraction in determining crystal symmetries. Multiple diffraction is phase-sensitive, so that the distinction between centro- and non-centro-symmetric space groups should be trivial in CBED: in addition, the stronger scattering of electrons may give a general increase in sensitivity to small atomic displacements. However, the sensitivity of CBED symmetry to the crystal point group has rarely been quantified, and CBED is also subject to symmetry-breaking due to local strains and inhomogeneities. The purpose of this paper is to classify the various types of symmetry-breaking, present calculations of the sensitivity, and illustrate symmetry-breaking by surface strains.CBED symmetry determinations usually proceed by determining the diffraction group along various zone axes, and hence finding the point group. The diffraction group can be found using either the intensity distribution in the discs

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Centrosome Aurora A gradient ensures single polarity axis in C. elegans embryos

Biochemical Society Transactions ◽

10.1042/bst20200298 ◽

2020 ◽

Vol 48 (3) ◽

pp. 1243-1253 ◽

Cited By ~ 1

Author(s):

Sukriti Kapoor ◽

Sachin Kotak

Keyword(s):

Symmetry Breaking ◽

Cell Fate ◽

Cell Cortex ◽

Axis Formation ◽

Aurora A Kinase ◽

Aurora A ◽

C Elegans ◽

Cell Embryo ◽

Polarity Establishment

Cellular asymmetries are vital for generating cell fate diversity during development and in stem cells. In the newly fertilized Caenorhabditis elegans embryo, centrosomes are responsible for polarity establishment, i.e. anterior–posterior body axis formation. The signal for polarity originates from the centrosomes and is transmitted to the cell cortex, where it disassembles the actomyosin network. This event leads to symmetry breaking and the establishment of distinct domains of evolutionarily conserved PAR proteins. However, the identity of an essential component that localizes to the centrosomes and promotes symmetry breaking was unknown. Recent work has uncovered that the loss of Aurora A kinase (AIR-1 in C. elegans and hereafter referred to as Aurora A) in the one-cell embryo disrupts stereotypical actomyosin-based cortical flows that occur at the time of polarity establishment. This misregulation of actomyosin flow dynamics results in the occurrence of two polarity axes. Notably, the role of Aurora A in ensuring a single polarity axis is independent of its well-established function in centrosome maturation. The mechanism by which Aurora A directs symmetry breaking is likely through direct regulation of Rho-dependent contractility. In this mini-review, we will discuss the unconventional role of Aurora A kinase in polarity establishment in C. elegans embryos and propose a refined model of centrosome-dependent symmetry breaking.

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