Kernel function and quantum algebras

By Boris Feigin, A. Hoshino, J. Shibahara, J. Shiraishi, S. Yanagida. 2010

53 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bb89c2a6e0d47d1573451f1efb429dafdfa95b28

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In Algebra and Number Theory

1. Boris Feigin
2. G. Merzon
3. M. Bershtein

In Geometry and Topology

1. Boris Feigin
2. G. Merzon
3. M. Bershtein

In Statistical and Nonlinear Physics

1. Boris Feigin
2. G. Merzon
3. M. Bershtein

Citations in the corpus

• Plane partitions with a “pit”: generating functions and representation theory (2015, background): “This tensor product was essentially elaborated in [17] which we follow.”