相关论文: Categorical Heisenberg action I: rational Cheredni…

We systematically apply semisimplification functors in modular representation theory. Motivated by the Duflo--Serganova functor in Lie superalgebras, we construct various functors of interest. In the setting of finite groups, we refine the…

In this survey article we review Kac-Moody and Heisenberg algebra actions on the categories $\mathcal{O}$ of the rational Cherednik algebras associated to groups $G(\ell,1,n)$. Using these actions we solve basic representation theoretic…

For every smooth projective variety, we construct an action of the Heisenberg algebra on the direct sum of the Grothendieck groups of all the symmetric quotient stacks which contains the Fock space as a subrepresentation. The action is…

Motivated by the work of of A. Zelevinsky on positive self-adjoint Hopf algebras, we define what we call a symmetric self-adjoint Hopf structure for a certain kind of semisimple abelian categories. It is known that every positive…

We show that the category O for a rational Cherednik algebra of type A is equivalent to modules over a q-Schur algebra (parameter not a half integer), providing thus character formulas for simple modules. We give some generalization to…

In this paper we categorify the Heisenberg action on the Fock space via the category O of cyclotomic rational double affine Hecke algebras. This permits us to relate the filtration by the support on the Grothendieck group of O to a…

Starting with a k-linear or DG category admitting a (homotopy) Serre functor, we construct a k-linear or DG 2-category categorifying the Heisenberg algebra of the numerical K-group of the original category. We also define a 2-categorical…

In this note we are interested in labelling the irreducible representations of non-semisimple specialisations of Hecke algebras of complex reflection groups. We will use category O for the rational Cherednik algebra and the KZ functor…

We first consider the rational Cherednik algebra corresponding to the action of a finite group on a complex variety, as defined by Etingof. We define a category of representations of this algebra which is analogous to "category O" for the…

We introduce and provide a classification theorem for the class of Heisenberg-Fock Leibniz algebras. This category of algebras is formed by those Leibniz algebras $L$ whose corresponding Lie algebras are Heisenberg algebras $H_n$ and whose…

We study reflexivity and structure properties of operator algebras generated by representations of the discrete Heisenberg semi-group. We show that the left regular representation of this semi-group gives rise to a semi-simple reflexive…

We prove that the KZ functor from a certain category of modules for the Cherednik algebra to finite dimensional modules over the Hecke algebra is essentially surjective. Then we begin to use this result to study the analog of category O for…

Ginzburg, Guay, Opdam and Rouquier established an equivalence of categories between a quotient category of the category $\mathcal{O}$ for the rational Cherednik algebra and the category of finite dimension modules of the Hecke algebra of a…

We construct an action of the Hecke monoid on the category of rational modules for the quantum negative Borel subgroup of the quantum general linear group. We also show that this action restricts to the category of polynomial modules for…

We determine the structure of category $\cO$ for the rational Cherednik algebra of $G(m,1,n)$ in the case where the $\KZ$ functor satisfies a condition called \emph{separating simples}. As a consequence, we show that the property of having…

The goal of this paper is to compute the supports of simple modules in the categories $\mathcal{O}$ for the rational Cherednik algebras associated to groups $G(\ell,1,n)$. For this we compute some combinatorial maps on the set of simples:…

We introduce a category of inverse semigroup actions and a category of \'etale groupoids. We show that there are three functors which send inverse semigroups to their spectral actions, inverse semigroup actions to their transformation…

We introduce a new algebra called the shifted $q=0$ affine algebra, which arises naturally from the study of coherent sheaves on Grassmannians and n-step partial flag varieties via a natural correspondence. It has similar presentation as…

We begin the study of unitary representations of Hecke algebras of complex reflections groups. We obtain a complete classification for the Hecke algebra of the symmetric group $\mathfrak{S}_n$ over the complex numbers. Interestingly, the…

We study the category O of representations of the rational Cherednik algebra A attached to a complex reflection group W. We construct an exact functor, called Knizhnik-Zamolodchikov functor, from O to the category of H-modules, where H is…