Symmetry-adapted liouville space: VII. Induced [formula omitted]n-symmetry over liouville space of | kqv〉〉 tensorial bases for nuclear spin- [formula omitted] clusters: A genealogical hierarchy under [formula omitted]-duality

Abstract

In examining nuclear spin dynamics of NMR spin clusters in density operator/generalized torque formalisms over | kqv〉〉 operator bases of Liouville space, it is necessary to consider the symmetry mappings and carrier spaces under a specialized group for such ( k i = 1) nuclear spin clusters. The SU2 × L n group provides the essential mappings and the form of H̃ carrier space, which allows one to: (a) draw comparisons with Hilbert space duality, and (b) outline the form of the Coleman-Kotani genealogical hierarchy under induced L n -symmetry. The simple-reducibility of the tensor space of k i = 1 recoupled tensors depends on a consideration of the v forms under SU2 ≈ SO(3) of these T kq ( v) bases, where v spans all { K̃…}( k 1- k n ) forms. The use of L n -combinatorial aspects, from the study of scalar invariants, and generalized word-length formalisms provide insight into the structure of explicit L n /SU2 bases. The value of such T kq ( v:[λ~]) comes from the way in which they allow the partitioning of the density operator σ( L n ) for multispin NMR problems and their φ k q ( v: [λ~])[ t] polarizations.