Abstract
We show that a deformation of Schur polynomials (matching the Shintani–Casselman–Shalika formula for the p-adic spherical Whittaker function) is obtained from a Hamiltonian operator on Fermionic Fock space. The discrete time evolution of this operator gives rise to states of a free-fermionic six-vertex model with boundary conditions generalizing the “domain wall boundary conditions,” which are not field-free. This is analogous to results of the Kyoto school in which ordinary Schur functions arise in the Boson–Fermion correspondence, and the Hamiltonian operator produces states of the five-vertex model. Our Hamiltonian arises naturally from super Clifford algebras studied by Kac and van de Leur. As an application, we give a new proof of a formula of Tokuyama [25] and Jacobi–Trudi type identities for the deformation of Schur polynomials. Variants leading to deformations of characters for other classical groups and their finite covers are also presented.
Original language | English (US) |
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Pages (from-to) | 100-121 |
Number of pages | 22 |
Journal | Journal of Combinatorial Theory. Series A |
Volume | 155 |
DOIs | |
State | Published - Apr 2018 |
Bibliographical note
Publisher Copyright:© 2017 Elsevier Inc.
Keywords
- Discrete time evolution
- Fock space
- Partition function
- Six-vertex model
- τ-functions