Coherent state construction of representations of osp(2|2) and primary fields of osp(2|2) conformal field theory

Generalized coherent states for q-oscillator connected with q-Hermite polynomials

“…. ., in full accordance with the recurrent relations (22). It is known (see [32]), that such defined operator X µ is symmetric and has indices of defect equal to (1, 1), so it has the family of the selfadjoint extensions.…”

“…An extensive bibliography (up to early 21st century) was given in the review [10]. Only in the last few months there appeared a number of interesting works devoted to generalization of vector coherent states for the case of matrix index ( [11]- [14]), hypergeometric [15] and combinatorial [16] coherent states,as well as to further development of mathematical [17,18] and physical [19,20] applications of coherent states, including applications to the description of models with exactly solvable potentials [21], super-symmetric conformal field theory [22] and to path integral [23] in holomorphic representation.…”

“…the moment problem for the Jacobi matrix, defined by the recurrent relations (22), is undetermined (see [32]) and the measure dµ(x) is determined not uniquely.…”

Finite dimensional irreducible representations of Lie superalgebra D (2, 1; α)

“…The nonlinear sigma models based on the supergroups have a vanishing oneloop β function, which are expected to be conformal invariant without adding the Wess-Zumino terms [14]. Finite-dimensional typical and atypical representations of osp(2|2) and gl (2|2) have been studied in several papers [15,16].…”

On gl 2|2 with hat (2) k Current Superalgebra and Twisted Conformal Field Theory

“…k were investigated in Refs. [20] ∼ [23]. The Kac-Moody superalgebra with twisted structure was considered only for the simplest superalgebra osp(2|2) (2) k with the vanishing of the super-dimension in Ref.…”