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2016

Rationality of capped descendent vertex in $K$-theory

Smirnov, Andrey

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In this paper we analyze the fundamental solution of the \textit{quantum difference equation} (qde) for the moduli space of instantons on two-dimensional projective space.

The qde is a $K$-theoretic generalization of the quantum differential equation in quantum cohomology.
As in the quantum cohomology case, the fundamental solution of qde provides the capping operator in $K$-theory (the rubber part of the capped vertex).
We study the dependence of the capping operator on the equivariant parameters $a_i$ of the torus acting on the instanton moduli space by changing the framing.

Rationality of capped descendent vertex in $K$-theory · Around

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Quantization of Lie groups and Lie algebras
N. Y. Reshetikhin, L. A. Takhtadzhyan, and L. D. Faddeev · 1989
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Notes on Macdonald polynomials and the geometry of Hilbert schemes
M. Haiman · 2002
Earlier work this paper cites.
Quantum cohomology of the Hilbert scheme of points in the plane
A. Okounkov and R. Pandharipande · 2010
Earlier work this paper cites.
The quantum differential equation of the Hilbert scheme of points in the plane
A. Okounkov and R. Pandharipande · 2010
Earlier work this paper cites.

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