Structure constants of Peterson Schubert calculus
arXiv:2508.05457
Abstract
We give an explicit, positive, and type-uniform formula for all equivariant structure constants of the Peterson Schubert calculus in arbitrary Lie types, using only the Cartan matrix of the corresponding root system . This solves an open problem originally asked by Harada--Tymoczko in type A for all Lie types. As an application, we derive a type-uniform formula for the mixed -Eulerian numbers.
25 pages, minor revisions. An extended abstract of this paper will appear in the Proceedings of the 38th Conference on Formal Power Series and Algebraic Combinatorics (Seattle). Comments are welcome!