The most degenerate irreducible representations of the symplectic group

1980 ◽  
Vol 21 (4) ◽  
pp. 630-635 ◽  
Author(s):  
M. K. F. Wong ◽  
Hsin‐Yang Yeh
Keyword(s):  
Symplectic Group ◽  
Irreducible Representations

RESTRICTIONS OF SOME REPRESENTATIONS OF THE SYMPLECTIC GROUP TO SUBGROUPS OF TYPE A1

2007 ◽  
Vol 06 (04) ◽  
pp. 697-701
Author(s):  
ANNA A. OSINOVSKAYA
Keyword(s):  
Algebraic Group ◽  
Symplectic Group ◽  
Algebraic Groups ◽  
Type A ◽  
Irreducible Representations ◽  
Symplectic Groups ◽  
Inductive System ◽  
Highest Weight ◽  
Composition Factors

Restrictions of modular irreducible representations of the symplectic algebraic group to naturally embedded long subgroups of type A1 are studied. Let ω = m1ω1 + ⋯ + mnωn be the highest weight of such representation. The composition factors of such restrictions are determined in the case of m1 + ⋯ + mn + 3 ≤ p < mn-1 + 2mn + 3 that completes the description of restrictions of classical algebraic groups to naturally embedded A1-subgroups and gives an example of a new inductive system of representations of symplectic groups that has no analogues in characteristic 0.

Genericity of Representations of p-Adic Sp2n and Local Langlands Parameters

2011 ◽  
Vol 63 (5) ◽  
pp. 1107-1136 ◽  
Author(s):  
Baiying Liu
Keyword(s):  
Local Field ◽  
Symplectic Group ◽  
Rational Points ◽  
Descent Method ◽  
Irreducible Representations ◽  
Local Factors ◽  
Langlands Parameters ◽  
Repre Sentations

Abstract Let G be the F-rational points of the symplectic group Sp2n, where F is a non-Archimedean local field of characteristic 0. Cogdell, Kim, Piatetski-Shapiro, and Shahidi constructed local Lang- lands functorial lifting from irreducible generic representations of G to irreducible representations of GL2n+1(F). Jiang and Soudry constructed the descent map from irreducible supercuspidal repre- sentations of GL2n+1(F) to those of G, showing that the local Langlands functorial lifting from the irreducible supercuspidal generic representations is surjective. In this paper, based on above results, using the same descent method of studying SO2n+1 as Jiang and Soudry, we will show the rest of local Langlands functorial lifting is also surjective, and for any local Langlands parameter , we construct a representation such that and ¾ have the same twisted local factors. As one application, we prove the G-case of a conjecture of Gross-Prasad and Rallis, that is, a local Langlands parameter is generic, i.e., the representation attached to is generic, if and only if the adjoint L-function of is holomorphic at s = 1. As another application, we prove for each Arthur parameter , and the corresponding local Langlands parameter , the representation attached to is generic if and only if is tempered.

Basis states for equivalent electrons. III. States for the Lie group SO(2l + 1) × SU(2) using Sp(4l + 2) states

1981 ◽  
Vol 59 (2) ◽  
pp. 207-212
Author(s):  
William R. Ross
Keyword(s):  
Irreducible Representation ◽  
Lie Group ◽  
Unitary Group ◽  
Symplectic Group ◽  
Irreducible Representations ◽  
Slater Basis

The Lie group SO(2l + 1) × EU(2) is a subgroup of the symplectic group Sp(4l + 2), which in turn is a subgroup of the unitary group U(4l + 2). The Slater basis states for N equivalent electrons form the basis for the irreducible representation (1N) of U(4l + 2). The basis states for the irreducible representations of SO(2l + 1) × SU(2) are expressed in terms of the states for irreducible representations of Sp(4l + 2). The basis states for SO(2l + 1) × SU(2) are also expressed in terms of the Slater basis states.

An Intuitive Method for the Determination of Crystal-Field Parameters in Laser Crystals

1993 ◽  
Vol 329 ◽  
Author(s):  
Frederick G. Anderson ◽  
H. Weidner ◽  
P. L. Summers ◽  
R. E. Peale ◽  
B. H. T. Chai
Keyword(s):  
Crystal Field ◽  
Irreducible Representations ◽  
Laser Crystals ◽  
Intuitive Method ◽  
Crystal Field Parameters ◽  
Intuitive Interpretation

AbstractExpanding the crystal field in terms of operators that transform as the irreducible representations of the Td group leads to an intuitive interpretation of the crystal-field parameters. We apply this method to the crystal field experienced by Nd3+ dopants in the laser crystals YLiF4, YVO4, and KLiYF5.

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.

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