Construction of basis vectors for symmetric irreducible representations of O(5) $ \supset$ O(3)

Abstract

A recursive method for construction of symmetric irreducible representations of O(2l + 1) in the O(2l + 1) ⊃ O(3) basis for identical boson systems is proposed. The formalism is realized based on the group chain U (2l + 1) ⊃ U (2l − 1) ⊗ U (2), of which the symmetric irreducible representations are simply reducible. The basis vectors of the O(2l + 1) ⊃ O(2l − 1) ⊗ U (1) can easily be constructed from those of 0) with resultant angular momentum quantum number L = 2τ + 2 − k for k = 0, 2, 3, · · · , 6 with a multiplicity 2 case for k = 6 are presented.

Alternative solvable description of the E(5) critical point symmetry in the interacting boson model

“…= 0, of which the corresponding eigenstates are not provided by the exact solution shown in (28). The results shown in (29) and (30) are only relevant to nuclear system in the large-N limit with equidistant spectrum in τ:…”

“…Solutions of (28) provide eigenvalues E (ζ ) τ,L and the corresponding eigenstates (24) simultaneously.…”

“…Therefore, (28) in this case results in a polynomial equation with variable E (ζ ) τ,L . The degree of the polynomial equals exactly to the dimension 1 2 (N − τ − τ s ) + 1 of the concerned Hilbert subspace.…”

“…basis vectors [28], which are orthonormal and multiplicityfree. Specifically, for given N, n d , and τ, the U( …”

An Elementary Derivation of the Matrix Elements of Real Irreducible Representations of so(3)

“…Recall that an embedding j : s → s of semisimple Lie algebras is called irreducible if the lowest dimensional irreducible representation Γ of s remains irreducible when restricted to s [11]. Irreducible embeddings play an important role in applications, as they allow one to construct bases of a Lie algebra s in terms of a basis of irreducibly-embedded subalgebras and irreducible tensor operators [12].…”