Mickelsson lowering operators for the symplectic group

1982 ◽  
Vol 23 (3) ◽  
pp. 347-349 ◽  
Author(s):  
Adam M. Bincer
Keyword(s):  
Symplectic Group ◽  
Lowering Operators

scholarly journals Families of abelian surfaces with real multiplication over Hilbert modular surfaces

1982 ◽  
Vol 88 ◽  
pp. 17-53 ◽  
Author(s):  
G. van der Geer ◽  
K. Ueno
Keyword(s):  
Endomorphism Ring ◽  
Symplectic Group ◽  
Abelian Surface ◽  
Quadratic Relation ◽  
Holomorphic Map ◽  
Real Multiplication ◽  
Compact Complex Surfaces ◽  
Hilbert Modular Surfaces ◽  
Hilbert Modular ◽  
Abelian Functions

Around the beginning of this century G. Humbert ([9]) made a detailed study of the properties of compact complex surfaces which can be parametrized by singular abelian functions. A surface parametrized by singular abelian functions is the image under a holomorphic map of a singular abelian surface (i.e. an abelian surface whose endomorphism ring is larger than the ring of rational integers). Humbert showed that the periods of a singular abelian surface satisfy a quadratic relation with integral coefficients and he constructed an invariant D of such a relation with respect to the action of the integral symplectic group on the periods.

-ADIC -FUNCTIONS FOR ORDINARY FAMILIES ON SYMPLECTIC GROUPS

2019 ◽  
Vol 19 (4) ◽  
pp. 1287-1347 ◽  
Author(s):  
Zheng Liu
Keyword(s):  
Eisenstein Series ◽  
Symplectic Group ◽  
Symplectic Groups ◽  
Simple Strategy ◽  
Doubling Method

We construct the $p$-adic standard $L$-functions for ordinary families of Hecke eigensystems of the symplectic group $\operatorname{Sp}(2n)_{/\mathbb{Q}}$ using the doubling method. We explain a clear and simple strategy of choosing the local sections for the Siegel Eisenstein series on the doubling group $\operatorname{Sp}(4n)_{/\mathbb{Q}}$, which guarantees the nonvanishing of local zeta integrals and allows us to $p$-adically interpolate the restrictions of the Siegel Eisenstein series to $\operatorname{Sp}(2n)_{/\mathbb{Q}}\times \operatorname{Sp}(2n)_{/\mathbb{Q}}$.

scholarly journals Construction and Characterization of Representations of SU(7) for GUT Model Builders

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1044
Author(s):  
Daniel Jones ◽  
Jeffery A. Secrest
Keyword(s):  
Gauge Symmetry ◽  
Symmetry Group ◽  
Lie Group ◽  
Cartan Subalgebra ◽  
Natural Extension ◽  
Grand Unification ◽  
Raising And Lowering Operators ◽  
Higher Dimensional ◽  
Lowering Operators

The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.

HAPPER'S CURIOUS DEGENERACIES AND YANGIAN

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1867-1873 ◽  
Author(s):  
CHENG-MING BAI ◽  
MO-LIN GE ◽  
KANG XUE
Keyword(s):  
Representation Theory ◽  
Algebraic Structure ◽  
Zeeman Effect ◽  
Tensor Space ◽  
Commutation Relations ◽  
Raising And Lowering Operators ◽  
Degenerate States ◽  
Lowering Operators

We find raising and lowering operators distinguishing the degenerate states for the Hamiltonian [Formula: see text] at x = ± 1 for spin 1 that was given by Happer et al.1,2 to interpret the curious degeneracies of the Zeeman effect for condensed vapor of 87 Rb . The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of Y(sl(2)).

scholarly journals Regular and residual Eisenstein series and the automorphic cohomology of Sp(2,2)

2009 ◽  
Vol 146 (1) ◽  
pp. 21-57 ◽  
Author(s):  
Harald Grobner
Keyword(s):  
Algebraic Group ◽  
Eisenstein Series ◽  
Symplectic Group ◽  
Automorphic Forms ◽  
General Theorem ◽  
Simple Algebraic Group ◽  
Ramanujan Conjecture ◽  
Eisenstein Cohomology ◽  
Derivatives Of

AbstractLetGbe the simple algebraic group Sp(2,2), to be defined over ℚ. It is a non-quasi-split, ℚ-rank-two inner form of the split symplectic group Sp8of rank four. The cohomology of the space of automorphic forms onGhas a natural subspace, which is spanned by classes represented by residues and derivatives of cuspidal Eisenstein series. It is called Eisenstein cohomology. In this paper we give a detailed description of the Eisenstein cohomologyHqEis(G,E) ofGin the case of regular coefficientsE. It is spanned only by holomorphic Eisenstein series. For non-regular coefficientsEwe really have to detect the poles of our Eisenstein series. SinceGis not quasi-split, we are out of the scope of the so-called ‘Langlands–Shahidi method’ (cf. F. Shahidi,On certainL-functions, Amer. J. Math.103(1981), 297–355; F. Shahidi,On the Ramanujan conjecture and finiteness of poles for certainL-functions, Ann. of Math. (2)127(1988), 547–584). We apply recent results of Grbac in order to find the double poles of Eisenstein series attached to the minimal parabolicP0ofG. Having collected this information, we determine the square-integrable Eisenstein cohomology supported byP0with respect to arbitrary coefficients and prove a vanishing result. This will exemplify a general theorem we prove in this paper on the distribution of maximally residual Eisenstein cohomology classes.

scholarly journals A demonstration that electroweak theory can violate parity automatically (leptonic case)

2018 ◽  
Vol 33 (04) ◽  
pp. 1830005 ◽  
Author(s):  
C. Furey
Keyword(s):  
Clifford Algebra ◽  
Ad Hoc ◽  
Higgs Bosons ◽  
Electroweak Theory ◽  
Ladder Operators ◽  
Raising And Lowering Operators ◽  
Ladder Operator ◽  
Left And Right ◽  
Electroweak Model ◽  
Lowering Operators

We bring to light an electroweak model which has been reappearing in the literature under various guises.[Formula: see text] In this model, weak isospin is shown to act automatically on states of only a single chirality (left). This is achieved by building the model exclusively from the raising and lowering operators of the Clifford algebra [Formula: see text]. That is, states constructed from these ladder operators mimic the behaviour of left- and right-handed electrons and neutrinos under unitary ladder operator symmetry. This ladder operator symmetry is found to be generated uniquely by [Formula: see text] and [Formula: see text]. Crucially, the model demonstrates how parity can be maximally violated, without the usual step of introducing extra gauge and extra Higgs bosons, or ad hoc projectors.

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