Séminaire Lotharingien de Combinatoire, B54j (2006), 13 pp.
Alain Goupil and Cedric Chauve
Combinatorial Operators for Kronecker Powers of Representations of Sn
Abstract.
We present combinatorial operators for the expansion of the
Kronecker product of irreducible representations of the symmetric
group Sn. These combinatorial operators are defined in the ring
of symmetric functions and act on the Schur functions basis. This
leads to a combinatorial description of the Kronecker powers of the
irreducible representations indexed with the partition
(n-1,1)
which specializes the concept of oscillating tableaux in Young's
lattice previously defined by S. Sundaram. We call our
specialization Kronecker tableaux. Their combinatorial
analysis leads to enumerative results for the multiplicity of
irreducible representations in the Kronecker powers of the forms
\chi(n-1,1)\otimes k and P\otimes k where P is the
permutation representation of Sn.
Received: September 30, 2005.
Revised: July 6, 2006.
Accepted: July 7, 2006.
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