Indecomposable Representations of the Square—Root Lie Algebras of Vector Type and Their Boson Realizations

摘要

The explicit expressions for indecomposable representations ofnine square-root Lie algebras of vector type,Rレイ (v,ィ = 0,+-1),are obtained on the space of universal enveloping algebra of two-state Heisenberg-Weyl algebra,the invariant subspaces and the quotient spaces.From Fock representations corresponding to these indecomposablerepresentations,the inhomogeneous boson realizations of are given.The expectation values of R in the angularmomentum coherent states are calculated as well as the corresponding classical limits.