arXiv subjects
Publications and source records attributed to Eilon Reisin-Tzur.
We show that the higher-dimensional Heegaard Floer homology between tuples of cotangent fibers and the conormal bundle of a homotopically nontrivial simple closed curve on $T^2$ recovers the polynomial representation of double affine Hecke algebra of type A. We also give a topological interpretation of Cherednik's inner product on the polynomial representation.
We construct an isomorphism between the wrapped higher-dimensional Heegaard Floer homology of $κ$-tuples of cotangent fibers and $κ$-tuples of conormal bundles of homotopically nontrivial simple closed curves in $T^*Σ$ with a certain braid skein group, where $Σ$ is a closed oriented surface of genus $> 0$ and $κ$ is a positive integer. Moreover, we show this produces a (right) module over the surface Hecke algebra associated to $Σ$. This module structure is shown to be equivalent to the polynomial representation of DAHA in the case where $Σ=T^2$ and the cotangent fibers and conormal bundles of curves are both parallel copies.