Reduced projection operators and algebraic expressions for the symmetry-adapted functions of the icosahedral group

Peng Dong Fan, Nanjing University
Jin Quan Chen, Nanjing University
J. P. Draayer, Louisiana State University


The algebraic expressions for the reduced projection operators ℘μ(λ)μ̄ = ∑i4=1uiβ̂i irreducible representation (irrep) λ of the icosahedral group I are found by using the double-induced technique and eigenfunction method, where β̂i, are the double-coset generators of I with respect to the cyclic subgroup C5. Simple algebraic expressions are derived for the symmetryadapted functions (SAF's) by applying the reduced projection operators ℘μ(λ)μ̄ to Ylm̄. The SAF's are functions of the angular momentum l, the quantum numbers λ, μ of the group chain I ⊃ C5 and the multiplicity label m̄. In this way, the SAP problem of the group I is solved once for all instead of for one angular momentum l each time. © 1999 International Union of Crystallography Printed in Great Britain - all rights reserved.