arXiv subjects

José Simental

Publications and source records attributed to José Simental.

22 records · Page 2Linked to original sources

arXiv2021

Algebra and geometry of link homology

These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply graded homology, its basic properties and recent advances, as well as three algebro-geometric models for link homology: braid varieties, Hilbert schemes of singular curves and affine Springer fibers, and Hilbert schemes of points on the plane.

math.AG↗

arXiv2021

Unitary representations of cyclotomic Hecke algebras at roots of unity: combinatorial classification and BGG resolutions

We relate the classes of unitary and calibrated representations of cyclotomic Hecke algebras and, in particular, we show that for the most important deformation parameters these two classes coincide. We classify these representations in terms of both multipartition combinatorics and as the points in the fundamental alcove under the action of an affine Weyl group. Finally, we cohomologically construct these modules via BGG resolutions.

math.RT↗

arXiv2021

Representations with minimal support for quantized Gieseker varieties

We study the minimally supported representations of quantizations of Gieseker moduli spaces. We relate them to $\operatorname{SL}_n$-equivariant D-modules on the nilpotent cone of $\mathfrak{sl}_n$ and to minimally supported representations of type A rational Cherednik algebras. Our main result is character formulas for minimally supported representations of quantized Gieseker moduli spaces.

math.RT↗

arXiv2017

Harish-Chandra bimodules over rational Cherednik algebras

We study Harish-Chandra bimodules over the rational Cherednik algebra $H_{c}(W)$ associated to a complex reflection group $W$ with parameter $c$. Our results allow us to partially reduce the study of these bimodules to smaller algebras. We classify those pairs of parameters $(c,c')$ for which there exist fully supported Harish-Chandra bimodules, and give a description of the category of all Harish-Chandra bimodules modulo those without full support. When $W$ is a symmetric group we are able to classify all irreducible Harish-Chandra bimodules. Our proofs are based on localization techniques, the action of the Namikawa-Weyl group on the set of parameters, and the study of partial KZ functors.

math.RT↗