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We study the algebra of invariant representative functions over the N-foldCartesian product of copies of a compact Lie group G modulo the action ofconjugation by the diagonal subgroup. We construct a basis of invariantrepresentative functions referred to as quasicharacters. The form of thequasicharacters depends on the choice of a reduction scheme. We determine themultiplication law of quasicharacters and express their structure constants interms of recoupling coefficients. Via this link, the choice of the reductionscheme acquires an interpretation in terms of binary trees. We show explicitlythat the structure constants decompose into products over primitive elements of9j symbol type. For SU(2), everything boils down to the combinatorics ofangular momentum theory. In the final part, we show that the above calculusenables us to calculate the matrix elements of bi-invariant operators occuringin quantum lattice gauge theory. In particular, both the quantum Hamiltonianand the orbit type relations may be dealt with in this way, thus, reducing boththe construction of the costratification and the study of the spectral problemto numerical problems in linear algebra. We spell out the spectral problem forG=SU(2) and we present sample calculations of matrix elements of orbit typerelations for the gauge groups SU(2) and SU(3). The methods developed may beuseful in the study of virtually all quantum models with polynomial constraintsrelated to some symmetry.

Quasicharacters, recoupling calculus and costratifications of lattice quantum gauge theory