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Abstract
We construct an infinite-dimensional Heisenberg algebra in the derived Hall algebra for the category of nilpotent representations of Jordan quiver. Using this Heisenberg algebra, we reconstruct the theory of symmetric functions, focusing on Hall-Littlewood symmetric functions and various operators acting on them.
Acknowledgements
This note is based on the master thesis of the first author. The second author thanks R. Kodera for the remark on the work of Hernandez and Leclerc [Citation3].
Additional information
Funding
The second author is supported by the Grant-in-aid for Scientific Research (No. 16K17570), JSPS. This work is also supported by the JSPS Bilateral Program “Topological Field Theory and String Theory – from topological recursion to quantum toroidal algebras”.