Heisenberg algebra, wedges and crystals

TL;DR

This paper explores the connection between Heisenberg algebra actions, q-deformed wedges, and crystal structures on multipartitions, providing explicit formulas and leveraging the boson-fermion correspondence.

Contribution

It introduces a new explicit formula for the Heisenberg crystal structure on charged multipartitions using boson-fermion correspondence.

Findings

Established the Heisenberg crystal structure on multipartitions.

Derived explicit formulas for the crystal computation.

Linked the algebraic actions to combinatorial structures.

Abstract

We explain how the action of the Heisenberg algebra on the space of q-deformed wedges yields the Heisenberg crystal structure on charged multipartitions, by using the boson-fermion correspondence and looking at the action of the Schur functions at q = 0. In addition, we give the explicit formula for computing this crystal in full generality.