• Corpus ID: 233394337

$\imath$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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