The University of Illinois Algebra-Geometry-Combinatorics Seminar
Spring 2024, Time: Thursdays 3-3:50PM, Place: Burrill Hall 124 / Altgeld Hall 345

Schubert Calculus and the Boson-Fermion Correspondence, Sylvester Zhang (University of Minnesota) -- February 22nd, 2024

Originally appeared in string theory, the Boson-Fermion correspondence has found linkage to symmetric functions, particularly through its application by the Kyoto school for deriving soliton solutions of the KP equations. In this framework, the space of Young diagrams is conceived as the Fermionic Fock space, while the ring of symmetric functions serves as the Bosonic Fock space. Then the (second part of) BF correspondence asserts that the map sending a partition to its Schur function forms an isomorphism as H-modules, with H being the Heisenberg algebra. In this talk, we give a generalization of this correspondence into the realm of Schubert calculus, wherein the space of infinite permutations plays the role of the fermionic space, and the ring of back-stable symmetric functions represents the bosonic space.

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The seminar co-organizers are Ian Cavey, Andrew Hardt, Shiliang Gao, Elizabeth Kelley, and Alexander Yong.