Understand
We introduce an analogue $K_n(x,z;q,t)$ of the Cauchy-type kernel function for the Macdonald polynomials, being constructed in the tensor product of the ring of symmetric functions and the commutative algebra $\mathcal{A}$ over the degenerate $\mathbb{C} \mathbb{P}^1$.
- We show that a certain restriction of $K_n(x,z;q,t)$ with respect to the variable $z$ is neatly described by the tableau sum formula of Macdonald polynomials.
- Next, we demonstrate that the integer level representation of the Ding-Iohara quantum algebra naturally produces the currents of the deformed $\mathcal{W}$ algebra.
- Then we remark that the $K_n(x,z;q,t)$ emerges in the highest-to-highest correlation function of the deformed $\mathcal{W}$ algebra.
Built on
I.G. Macdonald, Symmetric functions and Hall polynomials
1995
Earlier work this paper cites.
H. Awata, H. Kubo, S. Odake, J. Shiraishi, Quantum 𝒲 N {\mathcal{W}}_{N} algebras and Macdonald polynomials , Comm. Math. Phys. 179
1996
Earlier work this paper cites.
Similar
B. Feigin, E. Frenkel, Quantum 𝒲 \mathcal{W} -algebras and elliptic algebras , Comm. Math. Phys. 178
1996
Cited alongside, same era.
J. Shiraishi, H. Kubo, H. Awata, S. Odake, A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions , Lett. Math. Phys. 38
1996
Cited alongside, same era.
Then
J. Ding, K. Iohara, Generalization of Drinfeld quantum affine algebras , Lett. Math. Phys. 41
1997
Later among the works it cites.
B. Feigin, K. Hashizume, A. Hoshino, J. Shiraishi, S. Yanagida, A commutative algebra on degenerate ℂ ℙ 1 \mathbb{C}\mathbb{P}^{1} and Macdonald polynomials , J. Math. Phys. 50
2009
Later among the works it cites.
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