SCHUBERT PUZZLES AND INTEGRABILITY I: INVARIANT TRILINEAR FORMS

Abstract

The puzzle rules for computing Schubert calculus on d-step flag manifolds, proven in [Allen Knutson and Terence Tao, Puzzles and (equivariant) cohomology of Grassmannians, Duke Math. J. 119 (2003), pp. 221–260] for 1-step, by Anders Skovsted Buch, Andrew Kresch, Kevin Purbhoo, and Harry Tamvakis [J. Algebraic Combin. 44 (2016), pp. 973–1007] for 2-step, and conjectured by Izzet Coskun and Ravi Vakil [Geometricpositivity in the cohomology of homogeneous spaces and generalized Schubert calculus, Amer. Math. Soc., Providence, RI, 2009, pp. 77–124] for 3-step, lead to vector configurations (one vector for each puzzle edge label) that we recognize as the weights of some minuscule representations...