An explicit formula describing the branching of representations of sp(6) according to the reduction chain sp(6) ↓ sp(4) × sp(2) is given. This allows to classify the multiplicity free reductions and, moreover, obtain the multiplicity for each sp(4) × sp(2) representation. We compare the method with the approach based on the theory of S-functions, pointing out the strengths and weaknesses of the explicit formula. The branching rule is used to construct an orthogonal basis of eigenstates for sp(6), where degenerations are solved using a scalar instead of the standard missing label operator.

Keywords: representation of Lie groups, algebraic methods
PACS: 02.20.Qs, 02.40.Sv, 03.65.Fd

sp(6) ↓ sp(4) × sp(2) ŠAKOJIMOSI TAISYKLĖS IR TIKRINIŲ BŪSENŲ BAZĖS
R. Campoamor-Stursberg
Madrido Complutense universitetas, Madridas, Ispanija

Pateikta išreikštinė formulė, aprašanti sp(6) įvaizdžių šakojimąsi pagal redukcijos grandinėlę sp(6) ↓ sp(4) × sp(2). Tai leidžia klasifikuoti redukcijas, neturinčias pasikartojimų, bei gauti pasikartojimų skaičių kiekvienam sp(4) × sp(2) įvaizdžiui. Metodas palyginamas su tuo, kas gaunama remiantis S-funkcijų teorija, nurodant išreikštinės formulės privalumus ir trūkumus. Šakojimosi taisyklė panaudota sudaryti ortogonalią sp(6) tikrinių funkcijų bazę, kurioje išsigimimai sutvarkomi taikant skaliarą vietoje įprastinio trūkstamos žymos operatoriaus.

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