A reduced subduction graph and higher multiplicity in S_n transformation coefficients

Abstract

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.

12 pages, 1 figure, iopart class, Revisited version (several typographical errors have been corrected). Accepted for publication in J. Phys. A: Math. Gen

Cited by in corpus (2)

• Three-point Functions in $\mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence
• Combinatorics of transformations from standard to non-standard bases in Brauer algebras