Schubert polynomials and the boson-fermion correspondence

In the classical boson-fermion correspondence, the free fermionic Fock space F can be identified with the Hilbert space generated by Young diagrams and the bosonic Fock space B can be identified with the ring of symmetric functions. Then both F and B are representations of the Heisenberg algebra, and are isomorphic via the Schur functions. In this talk, we will present a partial generalization of this framework to Schubert calculus by interpreting permutations as certain 2D fermions with an action of the Heisenberg algebra, and by realizing Schubert polynomials as the time evolution of these 2D fermions. No prior knowledge will be assumed, though familiarity with symmetric functions will be helpful.

For information about the Richard P. Stanley Seminar in Combinatorics, visit https://math.mit.edu/combin/