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arXiv · 2309.07824

A Floer-theoretic interpretation of the polynomial representation of the double affine Hecke algebra

Eilon Reisin-Tzur
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Abstract

We construct an isomorphism between the wrapped higher-dimensional Heegaard Floer homology of $\kappa$-tuples of cotangent fibers and $\kappa$-tuples of conormal bundles of homotopically nontrivial simple closed curves in $T^*\Sigma$ with a certain braid skein group, where $\Sigma$ is a closed oriented surface of genus $> 0$ and $\kappa$ is a positive integer. Moreover, we show this produces a (right) module over the surface Hecke algebra associated to $\Sigma$. This module structure is shown to be equivalent to the polynomial representation of DAHA in the case where $\Sigma=T^2$ and the cotangent fibers and conormal bundles of curves are both parallel copies.

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Eilon Reisin-Tzur. 2023-09-14. A Floer-theoretic interpretation of the polynomial representation of the double affine Hecke algebra. https://arxiv.org/abs/2309.07824

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