Multiplicative formulas in Schubert calculus and quiver representation

Consider a flag variety XX and its cohomology ring H∗(X,Z) endowed with the Schubert basis. In [11], Richmond (2009) showed that some structure coefficients of the cup product in H∗(X,Z) are products of two such coefficients for smaller flag varieties. Consider a quiver without oriented cycle. If αα and ββ are two dimension vectors, α∘βα∘β denotes the number of αα-dimensional subrepresentations of a general α+βα+β-dimensional representation. In [5], Derksen and Weyman (in press) expressed some numbers α∘βα∘β as products of two such numbers for smaller dimension vectors. The aim of this work is to prove two generalizations of these two results by the same method.