Geodesic
Some Fock spaces with depth two action
Canadian journal of mathematics, Tome 77 (2025) no. 6, pp. 1890-1918

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DOI

The subject of this article is operators represented on a Fock space which act only on the two leading components of the tensor. We unify the constructions from [Ans07, BL09, BL11, LS08] and extend a number of results from these articles to our more general setting. The results include the quadratic relation satisfied by the kernel of the free cumulant generating function, the resolvent form of the generating function for the Wick polynomials, and classification results for the case when the vacuum state on the operator algebra is tracial. We handle the generating functions in infinitely many variables by considering their matrix-valued versions.
DOI : 10.4153/S0008414X24000555
Mots-clés : Fock space, free cumulants, Boolean cumulants, Wick polynomials 
Anshelevich, Michael; Mashburn, Jacob. Some Fock spaces with depth two action. Canadian journal of mathematics, Tome 77 (2025) no. 6, pp. 1890-1918. doi: 10.4153/S0008414X24000555
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     title = {Some {Fock} spaces with depth two action},
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     year = {2025},
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     doi = {10.4153/S0008414X24000555},
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