We establish the conjecture of Reiner and Yong for an explicit combinatorial formula for the expansion of a Grothendieck polynomial into the basis of Lascoux polynomials. This expansion is a subtle refinement of its symmetric function version due to Buch, Kresch, Shimozono, Tamvakis, and Yong, which gives the expansion of stable Grothendieck polynomials indexed by…

It is a classical result that the simple algebras in the category of finite dimensional vector spaces are precisely the n x n matrix algebras. The notion of algebras in more general tensor categories is easy to formulate, and we can ask for classification results in these categories. Such classification results have broad applications to conformal field…

The theory of P-partitions was developed by Stanley to understand/solve several enumerations problems and representations theory problems. Together with the work of Gessel, this led to the development of the space of quasisymmetric functions. Schur functions are naturally understood in the world of quasisymmetric functions as a sum over standard tableaux of Gessel fundamental functions.…