Specht modules decompose as alternating sums of restrictions of Schur modules.

Schur modules give the irreducible polynomial representations of the general linear group GL_t. Viewing the symmetric group S_tas a subgroup of GL_t, we may restrict Schur modules to S_t and decompose the result into a direct sum of Specht modules, the irreducible representations of S_t. We give an equivariant Möbius inversion formula that we use to invert this expansion in the representation ring for S_t for t large. In addition to explicit formulas in terms of plethysms, we show the coefficients that appear alternate in sign by degree. In particular, this allows us to define a new basis of symmetric functions whose structure constants are stable Kronecker coefficients and which expand with signs alternating by degree into the Schur basis. [ABSTRACT FROM AUTHOR]