scholarly journals Generic representations in L-packets

2016 ◽  
Vol 12 (06) ◽  
pp. 1613-1624
Author(s):  
Manish Mishra
Keyword(s):  
Group Action ◽  
Adjoint Group

We give the details of the construction of a map to restate a conjecture of Gan, Gross and Prasad about adjoint group action on generic representations in [Formula: see text]-packets. We give an application of the construction to give another proof of the classification of the Knapp–Stein [Formula: see text]-group associated to a unitary unramified character of a torus. Finally, we prove the conjecture for unramified [Formula: see text]-packets.

Dihedral group and classification of G-circuits of length 10

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Muhammad Nadeem Bari ◽  
Muhammad Aslam Malik ◽  
Saba Al-Kaseasbeh ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Alibek Issakhov ◽  
...  
Keyword(s):  
Cyclic Group ◽  
Group Action ◽  
Modular Group ◽  
Dihedral Group ◽  
Equivalence Classes ◽  
Quadratic Fields ◽  
Real Quadratic Fields ◽  
Exact Number ◽  
Real Quadratic

Abstract In this paper, we classify G-circuits of length 10 with the help of the location of the reduced numbers lying on G-circuit. The reduced numbers play an important role in the study of modular group action on P S L ( 2 , Z ) $PSL(2,\mathbb{Z})$ -subset of Q ( m ) \ Q $Q(\sqrt{m}){\backslash}Q$ . For this purpose, we define new notions of equivalent, cyclically equivalent, and similar G-circuits in P S L ( 2 , Z ) $PSL(2,\mathbb{Z})$ -orbits of real quadratic fields. In particular, we classify P S L ( 2 , Z ) $PSL(2,\mathbb{Z})$ -orbits of Q ( m ) \ Q $Q(\sqrt{m}){\backslash}Q$ = ⋃ k ∈ N Q * k 2 m $={\bigcup }_{k\in N}{Q}^{{\ast}}\left(\sqrt{{k}^{2}m}\right)$ containing G-circuits of length 10 and determine that the number of equivalence classes of G-circuits of length 10 is 41 in number. We also use dihedral group to explore cyclically equivalence classes of circuits and use cyclic group to explore similar G-circuits of length 10 corresponding to 10 of these circuits. By using cyclically equivalent classes of circuits and similar circuits, we obtain the exact number of G-orbits and the structure of G-circuits corresponding to cyclically equivalent classes. This study also helps us in classifying the reduced numbers lying in the P S L ( 2 , Z ) $PSL(2,\mathbb{Z})$ -orbits.

scholarly journals Moduli of toric vector bundles

2008 ◽  
Vol 144 (5) ◽  
pp. 1199-1213 ◽  
Author(s):  
Sam Payne
Keyword(s):  
Linear Group ◽  
Group Action ◽  
Chern Class ◽  
Vector Bundles ◽  
Closed Subscheme ◽  
Flag Varieties ◽  
Moduli Stack ◽  
Rank Conditions ◽  
Partial Flag Varieties

AbstractWe give a presentation of the moduli stack of toric vector bundles with fixed equivariant total Chern class as a quotient of a fine moduli scheme of framed bundles by a linear group action. This fine moduli scheme is described explicitly as a locally closed subscheme of a product of partial flag varieties cut out by combinatorially specified rank conditions. We use this description to show that the moduli of rank three toric vector bundles satisfy Murphy’s law, in the sense of Vakil. The preliminary sections of the paper give a self-contained introduction to Klyachko’s classification of toric vector bundles.

scholarly journals On the structure of open equivariant topological conformal field theories

2021 ◽  
Vol 127 (1) ◽  
pp. 63-78
Author(s):  
Ramsès Fernàndez-València
Keyword(s):  
Group Action ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

A classification of open equivariant topological conformal field theories in terms of Calabi-Yau $A_\infty $-categories endowed with a group action is presented.

Symmetry of the pentacene molecule and classification of electron states studied in the frame of group action on a set

Open Physics ◽  
2007 ◽  
Vol 5 (2) ◽  
Author(s):  
Piotr Potera ◽  
Ireneusz Stefaniuk ◽  
Marian Kuźma
Keyword(s):  
Group Theory ◽  
Group Action ◽  
Molecular State ◽  
Quantum States ◽  
Theory Method ◽  
Electron States ◽  
Factorization Scheme ◽  
Group Theory Method ◽  
The Subject

AbstractPentacene have recently become the subject of intense studies due to their physical properties which follow from the states of their outer-shell electrons that are able to take part in molecule bonding. The symmetry of these molecules provides the classification of quantum states according to the group theory method. In this paper, we apply a molecular state-space factorization scheme for the classification of pentacene molecules based on the structure of their electron states.

scholarly journals Icosahedral Group and Classification of PSL(2, Z)-Orbits of Real Quadratic Fields

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Tianlan Chen ◽  
Muhammad Nadeem Bari ◽  
Muhammad Aslam Malik ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Jia-Bao Liu
Keyword(s):  
Group Action ◽  
Modular Group ◽  
Equivalence Classes ◽  
Quadratic Fields ◽  
Real Quadratic Fields ◽  
Icosahedral Group ◽  
Real Quadratic

Reduced numbers play an important role in the study of modular group action on the PSL2,ℤ-subset of Qm/Q. For this purpose, we define new notions of equivalent, cyclically equivalent, and similar G-circuits in PSL2,ℤ-orbits of real quadratic fields. In particular, we classify PSL2,ℤ-orbits of Qm/Q=∪k∈NQ∗k2m containing G-circuits of length 6 and determine that the number of equivalence classes of G-circuits of length 6 is ten. We also employ the icosahedral group to explore cyclically equivalence classes of circuits and similar G-circuits of length 6 corresponding to each of these ten circuits. This study also helps us in classifying reduced numbers lying in the PSL2,ℤ-orbits.

Classification of the affine structures of a generalized quaternion group of order ⩾32{\geqslant 32}

2020 ◽  
Vol 23 (5) ◽  
pp. 847-869
Author(s):  
Wolfgang Rump
Keyword(s):  
Adjoint Group ◽  
Quaternion Group ◽  
Isomorphism Classes ◽  
Affine Structures ◽  
Generalized Quaternion Group ◽  
Generalized Quaternion

AbstractBased on computing evidence, Guarnieri and Vendramin conjectured that, for a generalized quaternion group G of order {2^{n}\geqslant 32}, there are exactly seven isomorphism classes of braces with adjoint group G. The conjecture is proved in the paper.

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

Diagnostic Value of Electron Microscopy in Soft Tissue Tumors

1970 ◽  
Vol 28 ◽  
pp. 220-221
Author(s):  
Gerald Fine ◽  
Azorides R. Morales
Keyword(s):  
Cardiac Myxoma ◽  
Osteogenic Sarcoma ◽  
Diagnostic Value ◽  
Soft Tissue Tumors ◽  
Amelanotic Melanoma ◽  
Growth Patterns ◽  
Light Microscopic Level ◽  
Mesenchymal Tumors ◽  
Good Agreement

For years the separation of carcinoma and sarcoma and the subclassification of sarcomas has been based on the appearance of the tumor cells and their microscopic growth pattern and information derived from certain histochemical and special stains. Although this method of study has produced good agreement among pathologists in the separation of carcinoma from sarcoma, it has given less uniform results in the subclassification of sarcomas. There remain examples of neoplasms of different histogenesis, the classification of which is questionable because of similar cytologic and growth patterns at the light microscopic level; i.e. amelanotic melanoma versus carcinoma and occasionally sarcoma, sarcomas with an epithelial pattern of growth simulating carcinoma, histologically similar mesenchymal tumors of different histogenesis (histiocytoma versus rhabdomyosarcoma, lytic osteogenic sarcoma versus rhabdomyosarcoma), and myxomatous mesenchymal tumors of diverse histogenesis (myxoid rhabdo and liposarcomas, cardiac myxoma, myxoid neurofibroma, etc.)

Ultrastructure of mesotheliomas

1984 ◽  
Vol 42 ◽  
pp. 98-101
Author(s):  
Irving Dardick
Keyword(s):  
Electron Microscopy ◽  
Latent Period ◽  
Spindle Cell ◽  
Spindle Cell Sarcoma ◽  
Metastatic Adenocarcinoma ◽  
Cell Sarcoma ◽  
Cytological Features ◽  
Industrial Use ◽  
Degree Of Differentiation

With the extensive industrial use of asbestos in this century and the long latent period (20-50 years) between exposure and tumor presentation, the incidence of malignant mesothelioma is now increasing. Thus, surgical pathologists are more frequently faced with the dilemma of differentiating mesothelioma from metastatic adenocarcinoma and spindle-cell sarcoma involving serosal surfaces. Electron microscopy is amodality useful in clarifying this problem.In utilizing ultrastructural features in the diagnosis of mesothelioma, it is essential to appreciate that the classification of this tumor reflects a variety of morphologic forms of differing biologic behavior (Table 1). Furthermore, with the variable histology and degree of differentiation in mesotheliomas it might be expected that the ultrastructure of such tumors also reflects a range of cytological features. Such is the case.

Sign in / Sign up

Export Citation Format

Share Document