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Explore a lecture by Matteo Mucciconi from the National University of Singapore as part of Harvard CMSA's program on Classical, quantum, and probabilistic integrable systems. Delve into the orthogonality properties of spin q-Whittaker polynomials, which are defined as partition functions of a solvable lattice model. Discover their mysterious properties including "unorthodox" symmetries, eigenrelations with respect to difference operators, and self-orthogonality. Learn about a novel orthogonality for Grothendieck polynomials from K-theory of Grassmannian, which emerges as a special case. The lecture also covers applications to exact solutions of directed random polymer models with Beta weights.
