A reduced subduction graph and higher multiplicity in S_n transformation coefficients

Details A reduced subduction graph and higher multiplicity in S_n transformation coefficients A reduced subduction graph and higher multiplicity in S_n transformation coefficients

2006-06-16

arxiv.org/abs/math-ph/0606037v3

J.Phys. A39 (2006) 12395-12406

Physics

Mathematical Physics

12 pages, 1 figure, iopart class, Revisited version (several typographical errors have been corrected). Accepted for publicati

Scientific paper

10.1088/0305-4470/39/40/008

Transformation coefficients between {\it standard} bases for irreducible representations of the symmetric group $S_n$ and {\it split} bases adapted to the $S_{n_1} \times S_{n_2} \subset S_n$ subgroup ($n_1 +n_2 = n$) are considered. We first provide a \emph{selection rule} and an \emph{identity rule} for the subduction coefficients which allow to decrease the number of unknowns and equations arising from the linear method by Pan and Chen. Then, using the {\it reduced subduction graph} approach, we may look at higher multiplicity instances. As a significant example, an orthonormalized solution for the first multiplicity-three case, which occurs in the decomposition of the irreducible representation $[4,3,2,1]$ of $S_{10}$ into $[3,2,1] \otimes [3,1]$ of $S_6 \times S_4$, is presented and discussed.

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