Bases for Irreducible Representations of the Unitary Group in the Symplectic Group Chain

1970 ◽  
Vol 11 (1) ◽  
pp. 162-168 ◽  
Author(s):  
V. Syamala Devi
Keyword(s):  
Unitary Group ◽  
Symplectic Group ◽  
Irreducible Representations

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.

scholarly journals Low codimensional embeddings of Sp(n) and Su(n)

1984 ◽  
Vol 27 (1) ◽  
pp. 25-29 ◽  
Author(s):  
G. Walker ◽  
R. M. W. Wood
Keyword(s):  
Euclidean Space ◽  
Lie Group ◽  
Maximal Torus ◽  
Unitary Group ◽  
Normal Bundle ◽  
Symplectic Group ◽  
Adjoint Representation ◽  
General Technique ◽  
Special Cases ◽  
Connected Lie Group

In [4] Elmer Rees proves that the symplectic group Sp(n) can be smoothly embedded in Euclidean space with codimension 3n, and the unitary group U(n) with codimension n. These are special cases of a result he obtains for a compact connected Lie group G. The general technique is first to embed G/T, where T is a maximal torus, as a maximal orbit of the adjoint representation of G, and then to extendto an embedding of G by using a maximal orbit of a faithful representation of G. In thisnote, we observe that in the cases G = Sp(n) or SU(n) an improved result is obtained byusing the “symplectic torus” S3 x … x S3 in place of T = S1 x … x S1. As in Rees's construction, the normal bundle of the embedding of G is trivial.

REPRESENTATIONS OF THE UNITARY GROUP AND WAVE FUNCTIONS

1961 ◽  
Vol 39 (4) ◽  
pp. 510-513
Author(s):  
H. A. Venables
Keyword(s):  
Spherical Harmonics ◽  
Unitary Group ◽  
Wave Functions ◽  
Irreducible Representations ◽  
Two Dimensional

A number of wave functions besides the spherical harmonics are obtainable from the irreducible representations of the two-dimensional unitary group.

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.

scholarly journals On Types for Unramified p-Adic Unitary Groups

2008 ◽  
Vol 60 (5) ◽  
pp. 1067-1107 ◽  
Author(s):  
Kazutoshi Kariyama
Keyword(s):  
Local Field ◽  
Unitary Group ◽  
Symplectic Group ◽  
Unitary Groups ◽  
Simple Type ◽  
Supercuspidal Representation ◽  
Fixed Field ◽  
Residue Characteristic

AbstractLet F be a non-archimedean local field of residue characteristic neither 2 nor 3 equipped with a galois involution with fixed field F0, and let G be a symplectic group over F or an unramified unitary group over F0. Following the methods of Bushnell–Kutzko for GL(N, F), we define an analogue of a simple type attached to a certain skew simple stratum, and realize a type in G. In particular, we obtain an irreducible supercuspidal representation of G like GL(N, F).

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