Journal of Algebraic Combinatorics

, Volume 49, Issue 1, pp 99–124 | Cite as

Heisenberg algebra, wedges and crystals

  • Thomas GerberEmail author


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.


Fock space Categorification Quantum groups Heisenberg algebra Crystals Symmetric functions Combinatorics 



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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Authors and Affiliations

  1. 1.Lehrstuhl D für MathematikRWTH Aachen UniversityAachenGermany

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