Branching rules for representations of classical Lie groups

1990 ◽  
Vol 84 (1) ◽  
pp. 675-682
Author(s):  
V. D. Lyakhovskii ◽  
I. A. Filanovskii
Keyword(s):  
Lie Groups ◽  
Branching Rules

Lie Groups and the Jahn–Teller Effect

1974 ◽  
Vol 52 (11) ◽  
pp. 999-1044 ◽  
Author(s):  
B. R. Judd
Keyword(s):  
Lie Groups ◽  
Nuclear Physics ◽  
Angular Frequency ◽  
Teller Effect ◽  
Octahedral Complex ◽  
Noncompact Group ◽  
Five Dimensions ◽  
Branching Rules ◽  
Jahn Teller ◽  
Jahn Teller Effect

After an introduction to the classic theory of the Jahn–Teller effect for octahedral complexes, an account is given of Lie groups and their relevance to the F+ center in CaO. The coincidence of the three-fold and two-fold vibrational modes (both of angular frequency ω) leads to a study of U5 and R5, the unitary and rotation groups in five dimensions. The language of second quantization is used to describe the weight spaces and branching rules. Pairs of annihilation and creation operators for phonons are coupled to zero angular momentum and used as the generators of the noncompact group O(2, 1). This facilitates the evaluation of matrix elements of V, the interaction that couples the oscillations of the octahedral complex to the electron in its interior. Glauber states are used near the strong Jahn–Teller limit, corresponding to [Formula: see text]. The possible extension of the analysis to incorporate the breathing mode is outlined. Correspondences with problems in nuclear physics are mentioned.

scholarly journals Basic Properties of the Exceptional Lie Groups

1977 ◽  
Vol 30 (3) ◽  
pp. 259 ◽  
Author(s):  
BG Wybourne ◽  
MJ Bowick
Keyword(s):  
Elementary Particle ◽  
Lie Groups ◽  
Schur Functions ◽  
Computer Algorithms ◽  
Kronecker Products ◽  
Basic Properties ◽  
Exceptional Groups ◽  
Important Group ◽  
Branching Rules ◽  
Exceptional Lie Groups

The exceptional Lie groups playa significant role in elementary particle models involving octonionic coloured quark fields. Simple methods for calculating the basic properties of these groups are outlined here. Among the properties computed are the dimensions and Dynkin index eigenvalues of irreps and branching rules for the most important group-subgroup structures. Kronecker products and symmetrized Kronecker powers of irreps of the exceptional groups are resolved. The concepts of elementary multiplets and Schur functions (S-functions) are used to greatly simplify the calculations, making possible manual calculations that are well beyond the capabilities of modem computer algorithms based on the enumeration of weights.

Branching Rules for Simple Lie Groups

1965 ◽  
Vol 6 (10) ◽  
pp. 1534-1539 ◽  
Author(s):  
M. L. Whippman
Keyword(s):  
Lie Groups ◽  
Simple Lie Groups ◽  
Branching Rules
Sign in / Sign up

Export Citation Format

Share Document