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arXiv · 1510.06116

Permutation-equivariant quantum K-theory VIII. Explicit reconstruction

Alexander Givental
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Abstract

In Part VII, we proved that the range of the big J-function in permutation-equivariant genus-0 quantum K-theory is an overruled cone, and gave its adelic characterization. Here we show that the ruling spaces are D_q-modules in Novikov's variables, and moreover, that the whole cone is invariant under a large group of symmetries defined in terms of q-difference operators. We employ this for the explicit reconstruction of the cone from one point on it, and apply the result to toric target spaces, when such a point is given by the q-hypergeometric function.

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Alexander Givental. 2015-10-21. Permutation-equivariant quantum K-theory VIII. Explicit reconstruction. https://arxiv.org/abs/1510.06116

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