scholarly journals Lifting of characters on p-adic orthogonal and metaplectic groups

2010 ◽  
Vol 146 (3) ◽  
pp. 795-810 ◽  
Author(s):  
Tatiana K. Howard
Keyword(s):  
Transfer Factor ◽  
Orthogonal Group ◽  
Symplectic Group ◽  
Dual Pair ◽  
Metaplectic Groups ◽  
Oscillator Representation ◽  
Parabolic Induction ◽  
The Difference ◽  
Metaplectic Cover ◽  
Split Orthogonal Group

AbstractLet F be a p-adic field. Consider a dual pair $({\rm SO}(2n+1)_+, \widetilde {{\rm Sp}}(2n)),$ where SO(2n+1)+ is the split orthogonal group and $\widetilde {{\rm Sp}}(2n)$ is the metaplectic cover of the symplectic group Sp(2n) over F. We study lifting of characters between orthogonal and metaplectic groups. We say that a representation of SO(2n+1)+ lifts to a representation of $\widetilde {{\rm Sp}}(2n)$ if their characters on corresponding conjugacy classes are equal up to a transfer factor. We study properties of this transfer factor, which is essentially the character of the difference of the two halves of the oscillator representation. We show that the lifting commutes with parabolic induction. These results were motivated by the paper ‘Lifting of characters on orthogonal and metaplectic groups’ by Adams who considered the case F=ℝ.

Poles ofL-functions and theta liftings for orthogonal groups

2009 ◽  
Vol 8 (4) ◽  
pp. 693-741 ◽  
Author(s):  
David Ginzburg ◽  
Dihua Jiang ◽  
David Soudry
Keyword(s):  
Eisenstein Series ◽  
Orthogonal Group ◽  
Symplectic Groups ◽  
Orthogonal Groups ◽  
Metaplectic Groups ◽  
Automorphic Representations ◽  
Domain Of Holomorphy ◽  
First Occurrence ◽  
Cuspidal Automorphic Representations

AbstractIn this paper, we prove that the first occurrence of global theta liftings from any orthogonal group to either symplectic groups or metaplectic groups can be characterized completely in terms of the location of poles of certain Eisenstein series. This extends the work of Kudla and Rallis and the work of Moeglin to all orthogonal groups. As applications, we obtain results about basic structures of cuspidal automorphic representations and the domain of holomorphy of twisted standardL-functions.

SYMPLECTIC SPACE OR ORTHOGONAL SPACE OF n QUBITS

2011 ◽  
Vol 09 (06) ◽  
pp. 1449-1457
Author(s):  
JIAN-WEI XU
Keyword(s):  
Hilbert Space ◽  
Orthogonal Group ◽  
Symplectic Group ◽  
Orthonormal Basis ◽  
Mathematical Structure ◽  
Symplectic Space ◽  
Orthogonal Space ◽  
Spin Flip

In Hilbert space of n qubits, we introduce symplectic space (n odd) or orthogonal space (n even) via the spin-flip operator. Under this mathematical structure we discuss some properties of n qubits, including homomorphically mapping local operations of n qubits into symplectic group or orthogonal group, and proving that the generalized "magic basis" is just the biorthonormal basis (i.e. the orthonormal basis of both Hilbert space and the orthogonal space). Finally, a demonstrated example is given to discuss the application in physics of this mathematical structure.

scholarly journals Parabolic induction and Jacquet functors for metaplectic groups

2010 ◽  
Vol 323 (1) ◽  
pp. 241-260 ◽  
Author(s):  
Marcela Hanzer ◽  
Goran Muić
Keyword(s):  
Metaplectic Groups ◽  
Parabolic Induction

scholarly journals On invariant theory under restricted groups

1944 ◽  
Vol 239 (809) ◽  
pp. 387-417 ◽  
Keyword(s):  
Invariant Theory ◽  
Orthogonal Group ◽  
Symplectic Group ◽  
Transformation Groups ◽  
Characteristic Analysis ◽  
Linear Complex ◽  
Group Integration ◽  
Group A ◽  
Quadratic Complex

A previous paper, ‘Invariant theory, tensors and group characters’, dealt with invariant theory under the full linear group. In this paper the methods are extended to restricted groups of transformation such as the orthogonal group. A knowledge of the characters of the group is shown to be an essential preliminary to any adequate study of invariants under the group. The characters of the orthogonal and symplectic groups, previously obtained by Schur and Weyl by transcendental methods involving group integration, are here obtained by methods entirely algebraic. Concerning transformation groups with a system of fundamental tensors, a fundamental theorem is proved that every concomitant may be obtained by multiplication and contraction of ground-form tensors, tensor variables, fundamental tensors and the alternating tensor. A characteristic analysis is developed, involving the operation denoted by ®, which enables the numbers and types of the concomitants of any given degree in any system of ground forms to be predicted. The determination of the actual concomitants is also discussed. Application is made for the orthogonal group to the quadratic, the ternary cubic and the quaternary quadratic complex; for the ternary symplectic group, to the quadratic, the linear complex and the quadratic complex. Various applications are also made for intransitive and imprimitive groups of transformation.

On Induced Representations Distinguished by Orthogonal Groups

2013 ◽  
Vol 56 (3) ◽  
pp. 647-658 ◽  
Author(s):  
Cesar Valverde
Keyword(s):  
Irreducible Representation ◽  
Characteristic Zero ◽  
Orthogonal Group ◽  
Orthogonal Groups ◽  
Induced Representations ◽  
Supercuspidal Representations ◽  
Parabolic Induction

Abstract.LetFbe a local non-archimedean field of characteristic zero. We prove that a representation ofGL(n,F) obtained from irreducible parabolic induction of supercuspidal representations is distinguished by an orthogonal group only if the inducing data is distinguished by appropriate orthogonal groups. As a corollary, we get that an irreducible representation induced from supercuspidals that is distinguished by an orthogonal group is metic.

scholarly journals Split Orthogonal Group: A Guiding Principle for Sign-Problem-Free Fermionic Simulations

2015 ◽  
Vol 115 (25) ◽  
Author(s):  
Lei Wang ◽  
Ye-Hua Liu ◽  
Mauro Iazzi ◽  
Matthias Troyer ◽  
Gergely Harcos
Keyword(s):  
Orthogonal Group ◽  
Guiding Principle ◽  
Sign Problem ◽  
Group A ◽  
Split Orthogonal Group

Lung function of healthy young men in India: contributory roles of genetic and environmental factors

1975 ◽  
Vol 191 (1104) ◽  
pp. 413-425 ◽  
Keyword(s):  
Lung Function ◽  
Transfer Factor ◽  
Haemoglobin Concentration ◽  
Young Men ◽  
New Guinea ◽  
Forced Expiratory Volume ◽  
North India ◽  
South Indian ◽  
The Difference ◽  
Genetic And Environmental Factors

The forced expiratory volume and vital capacity, the total lung capacity and sub-divisions and the lung transfer factor for carbon monoxide and its sub-divisions have been measured on 122 young men living near Delhi, including Servicemen from Gurkha, Rajput and south Indian regiments and civilians mainly from north India. The findings, standardized for age and stature and in the case of the transfer factor the smoking habits, the haemoglobin concentration and the tension of oxygen in the alveolar capillaries, have been compared with those for European and New Guinea men studied by similar methods and with data reported in the literature for other inhabitants of the Indian sub-continent. The lung function of the present Gurkha highlanders is superior to that of the Indian lowlanders and resembles that of both New Guinea highlanders living at an altitude of approximately 1800 m and men from Bhutan (altitude 3100 m). The Rajputs and other north Indians have slightly larger lungs than the men from south India; the lung function of the latter subjects resembles that of the New Guinea coastal dwellers. All these lowland subjects have lungs which are materially smaller than those of Europeans. The observed differences may be explained in terms of a genetic factor which contributes to the relatively large lung of people of European descent and an environmental factor, probably related to physical activity during childhood, which contributes to the superior lung function of hill people. The possible survival value in an inhospitable environment of large and permeable lungs may also have contributed to the difference, but the magnitude of this effect is probably small.

scholarly journals The impact of changing to the Global Lung Function Initiative reference equations for transfer factor in paediatrics

2020 ◽  
pp. 00412-2020
Author(s):  
Paul D. Burns ◽  
James Y. Paton
Keyword(s):  
Carbon Monoxide ◽  
Lung Function ◽  
Paediatric Patient ◽  
Transfer Factor ◽  
Reference Equations ◽  
The Difference ◽  
Predicted Values ◽  
Age Range ◽  
The Impact ◽  
Interpretation Of Results

The Global Lung Function Initiative (GLI) all age reference equations for carbon monoxide transfer factor were published in 2017 and endorsed by the ERS/ATS. In order to understand the impact of these new reference equations on the interpretation of results in children referred from haematology and oncology paediatric services, we retrospectively analysed transfer factor results from any paediatric patient referred from haematology oncology in the period 2010–2018. We examined TLCO, KCO and VA from 241 children (age range; 7–18, 130 male). The predicted values from Rosenthal and GLI were plotted against height. The difference in interpretation of results was analysed by looking at the percentage of patients <LLN for each parameter. Overall, the Rosenthal predicted values for TLCO were higher than GLI. Predicted KCO using Rosenthal was higher in all observations. In contrast, the Rosenthal predicted VA was generally lower than the GLI value. The GLI predicted values for transfer factor show considerable differences compared with currently used paediatric UK reference values, differences that will have a significant impact on interpretation of results.

scholarly journals Howe duality of Higgs – Hahn algebra for 8D harmonic oscillator

2019 ◽  
Vol 55 (2) ◽  
pp. 216-224
Author(s):  
А. N. Lavrenov ◽  
I. A. Lavrenov
Keyword(s):  
Tensor Product ◽  
Harmonic Oscillator ◽  
Symmetry Algebra ◽  
Dual Pair ◽  
Two Dimensions ◽  
Discrete Version ◽  
Oscillator Representation ◽  
Higgs Algebra ◽  
Howe Duality ◽  
The One

In the light of the Howe duality, two different, but isomorphic representations of one algebra as Higgs algebra and Hahn algebra are considered in this article. The first algebra corresponds to the symmetry algebra of a harmonic oscillator on a 2-sphere and a polynomially deformed algebra SU(2), and the second algebra encodes the bispectral properties of corresponding homogeneous orthogonal polynomials and acts as a symmetry algebra for the Hartmann and certain ring-shaped potentials as well as the singular oscillator in two dimensions. The realization of this algebra is shown in explicit form, on the one hand, as the commutant O(4) ⊕ O(4) of subalgebra U(8) in the oscillator representation of universal algebra U (u(8)) and, on the other hand, as the embedding of the discrete version of the Hahn algebra in the double tensor product SU(1,1) ⊗ SU(1,1). These two realizations reflect the fact that SU(1,1) and U(8) form a dual pair in the state space of the harmonic oscillator in eight dimensions. The N-dimensional, N-fold tensor product SU(1,1)⊗N аnd q-generalizations are briefly discussed.

scholarly journals Transfert d’intégrales orbitales pour le groupe métaplectique

2010 ◽  
Vol 147 (2) ◽  
pp. 524-590 ◽  
Author(s):  
Wen-Wei Li
Keyword(s):  
Trace Formula ◽  
Local Field ◽  
Transfer Factor ◽  
Characteristic Zero ◽  
Prior Work ◽  
Selberg Trace Formula ◽  
Metaplectic Groups ◽  
Orbital Integrals ◽  
Fundamental Lemma ◽  
Set Up

AbstractWe set up a formalism of endoscopy for metaplectic groups. By defining a suitable transfer factor, we prove an analogue of the Langlands–Shelstad transfer conjecture for orbital integrals over any local field of characteristic zero, as well as the fundamental lemma for units of the Hecke algebra in the unramified case. This generalizes prior work of Adams and Renard in the real case and serves as a first step in studying the Arthur–Selberg trace formula for metaplectic groups.

Sign in / Sign up

Export Citation Format

Share Document