# $\imath$Hall algebra of Jordan quiver and $\imath$Hall-Littlewood functions

@inproceedings{Lu2021imathHallAO, title={\$\imath\$Hall algebra of Jordan quiver and \$\imath\$Hall-Littlewood functions}, author={Ming Lu and Shiquan Ruan and Weiqiang Wang}, year={2021} }

We show that the ıHall algebra of the Jordan quiver is a polynomial ring in infinitely many generators and obtain transition relations among several generating sets. We establish a ring isomorphism from this ıHall algebra to the ring of symmetric functions in two parameters t, θ, which maps the ıHall basis to a class of (modified) inhomogeneous Hall-Littlewood (ıHL) functions. The (modified) ıHL functions admit a formulation via raising and lowering operators. We formulate and prove Pieri rules…

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