Free fermions and Schur expansions of multi-Schur functions
arXiv:2105.02604 · doi:10.1016/j.jcta.2023.105767
Abstract
Multi-Schur functions are symmetric functions that generalize the supersymmetric Schur functions, the flagged Schur functions, and the refined dual Grothendieck functions, which have been intensively studied by Lascoux. In this paper, we give a new free-fermionic presentation of them. The multi-Schur functions are indexed by a partition and two ``tuples of tuples'' of indeterminates. We construct a family of linear bases of the fermionic Fock space that are indexed by such data and prove that they correspond to the multi-Schur functions through the boson-fermion correspondence. By focusing on some special bases, which we call refined bases, we give a straightforward method of expanding a multi-Schur function in the refined dual Grothendieck polynomials. We also present a sufficient condition for a multi-Schur function to have its Hall-dual function in the completed ring of symmetric functions.
arXiv comment18 pages
References in corpus (12)
- Free fermions and tau-functions
- Vertex models, TASEP and Grothendieck polynomials
- K-theoretic boson-fermion correspondence and melting crystals
- Duality and deformations of stable Grothendieck polynomials
- Grothendieck polynomials and the Boson-Fermion correspondence
- Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions
- Refined dual Grothendieck polynomials, integrability, and the Schur measure
- Free-fermions and skew stable Grothendieck polynomials
- Neutral-fermionic presentation of the -theoretic -function
- Determinantal formulas for dual Grothendieck polynomials
- Refined canonical stable Grothendieck polynomials and their duals, Part 1
- Jacobi--Trudi formulas for flagged refined dual stable Grothendieck polynomials