# Heisenberg algebra, wedges and crystals

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## 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.

## Keywords

Fock space Categorification Quantum groups Heisenberg algebra Crystals Symmetric functions Combinatorics## Notes

### Acknowledgements

Many thanks to Emily Norton for pointing out an inconsistency in the first version of this paper and for helpful conversations.

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