STANDARD TABLEAUX AND KRONECKER PROJECTIONS OF SPECHT MODULES

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International Electronic Journal of Algebra
Volume:10 Issue:10
STANDARD TABLEAUX AND KRONECKER PROJECTIONS OF SPECHT MODULES

STANDARD TABLEAUX AND KRONECKER PROJECTIONS OF SPECHT MODULES

Authors : Jaydeep Chipalkatti, Tagreed Mohammed

Pages : 123-150

View : 40 | Download : 5

Publication Date : 2011-12-01

Article Type : Research Paper

Abstract :Given a partition λ of a positive integer d, let Vλ denote the corresponding irreducible rational representation of the symmetric group Sd. When λ is a hook partition or a two-rowed partition, we explicitly describe the equivariant morphism Vλ ⊗ Vλ −→ Vinsert ignore into journalissuearticles values(d); in terms of the standard tableau basis of Vλ. We give similar descriptions for the morphism Vλ ⊗ Vλ′ −→ Vinsert ignore into journalissuearticles values(1d);, as well as for the projection morphisms onto the irreducible factors of the tensor product Vinsert ignore into journalissuearticles values(d−1,1); ⊗ Vinsert ignore into journalissuearticles values(d−1,1);. Our results can be interpreted as giving formulae for certain Clebsch-Gordan coefficients for the symmetric group.
Keywords : Clebsch Gordan coefficients, Kronecker product, Specht module

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