The Peterson variety is a remarkable subvariety of the flag variety, introduced by Dale Peterson to realize the quantum cohomology rings of all (Langlands dual) partial flag varieties geometrically. Harada and Tymoczko posed the open problem (in type A) of finding a positive formula for the structure constants of the cohomology ring of the Peterson variety. 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 Φ. As an application, we derive a type-uniform formula for the mixed Φ-Eulerian numbers.

桂弢，西湖大学理论科学研究院博士后。2018年本科毕业于四川大学数学学院，2023年于中国科学院数学与系统科学研究院获得博士学位，师从席南华研究员。主要研究方向是李理论、表示论、组合代数几何与组合霍奇理论。