Skew RSK and coincidence of Littlewood-Richardson commutors

Olga Azenhas
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 Positivity of Littlewood-Richardson coefficients in existence problems. There exist d × d non singular matrices A, B and C , over a local principal ideal domain, with Smith invariants µ, ν and λ
more » ... iants µ, ν and λ respectively, such that AB = C iff c λ µ ν > 0. / 29 Coincidence of LR commutors Problem (Pak, Vallejo'04). Show that all LR commutors are involutions and coincide. One has several LR commutors and all are involutions. One involution needs to be included in the coincidence list : Goal: Internal insertion LR commutor coincides with switching LR commutor. 6 / 29