https://doi.org/10.1140/epjc/s10052-023-11765-8
Regular Article - Theoretical Physics
Symmetric deformed 2D/3D Hurwitz–Kontsevich model and affine Yangian of 
1
School of Mathematics and Statistics, Henan University, 475001, Kaifeng, China
2
School of Mathematical Sciences, Capital Normal University, 100048, Beijing, China
Received:
26
January
2023
Accepted:
26
June
2023
Published online:
17
July
2023
Since the (
-deformed) Hurwitz Kontsevich model corresponds to the special case of affine Yangian of . In this paper, we construct two general cases of the -deformed Hurwitz Kontsevich model. We find that the W-operators of these two models can be represented by the generators 
of the affine Yangian of , and the eigenstates (the symmetric functions 
and 3-Jack polynomials) can be obtained from the 3D Young diagram representation of affine Yangian of . Then we can see that the W-operators and eigenstates are symmetric about the permutations of coordinate axes.
© The Author(s) 2023
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