Free fermions and Schur expansions of multi-Schur functions

Multi-Schur functions are symmetric that generalize the supersymmetric Schur functions, flagged and refined dual Grothendieck which have been intensively studied by Lascoux. In this paper, we give a new free-fermionic presentation of them. The multi-Schur indexed partition two ``tuples tuples'' indeterminates. We construct family linear bases fermionic Fock space such data prove they correspond to through boson-fermion correspondence. By focusing on some special bases, call straightforward method expanding function in polynomials. also present sufficient condition for its Hall-dual completed ring functions.