Stanley Symmetric Functions and Quiver Varieties

We prove that the coefficients obtained when Stanley symmetric functions are expanded in the basis of Schur functions are special cases of the coefficients in the formula for quiver varieties given by the author and W. Fulton (1999, Invent. Math.135, 665–687), and we discuss the relations of this with a conjectured Littlewood–Richardson rule for these quiver coefficients. In addition we generalize a factorization formula for Schubert polynomials of a product of two permutations.