Skew RSK and coincidence of Littlewood-Richardson commutors

Olga Azenhas
unpublished
These numbers c λ µ,ν also arise as tensor product multiplicities. Schur polynomials s λ (x) may be interpreted as irreducible characters of the general linear group GL d (C). The decomposition of the tensor product of two irreducible polynomial representations V µ and V ν of the general linear group GL d (C) into irreducible representations of GL d (C), is given by Positivity of Littlewood-Richardson coefficients in existence problems. There exist d × d non singular matrices A, B and C , over
more » ... local principal ideal domain, with Smith invariants µ, ν and λ respectively, such that AB = C iff c λ µ ν > 0.
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