相关论文: Proof of Varagnolo-Vasserot conjecture on cyclotom…

Varagnolo and Vasserot conjectured an equivalence between the category O for a cyclotomic Rational Cherednik algebra and a truncation of an affine parabolic category O of type A. In this paper we reduce their conjecture to some purely…

Varagnolo and Vasserot conjectured an equivalence between the category O for CRDAHA's and a subcategory of an affine parabolic category O of type A. We prove this conjecture. As applications, we prove a conjecture of Rouquier on the…

We prove a conjecture of Rouquier relating the decomposition numbers in category $\mathcal{O}$ for a cyclotomic rational Cherednik algebra to Uglov's canonical basis of a higher level Fock space. Independent proofs of this conjecture have…

We study equivalences for category O_p of the rational Cherednik algebras H_p of type G_l(n) = \mu_l^n\rtimes S_n: a highest weight equivalence between O_p and O_{\sigma(p)} for \sigma\in S_l and an action of S_l on a non-empty Zariski open…

Let W be a complex reflection group and H_c(W) the Rational Cherednik algebra for $W$ depending on a parameter c. One can consider the category O for H_c(W). We prove a conjecture of Rouquier that the categories O for H_c(W) and H_{c'}(W)…

We introduce parabolic induction and restriction functors for rational Cherednik algebras, and study their basic properties. Then we discuss applications of these functors to representation theory of rational Cherednik algebras. In…

We prove that the K-theory of an exact quasicategory can be computed via a higher categorical variant of the Q construction. This construction yields a quasicategory whose weak homotopy type is a delooping of the K-theory space. We show…

Using the orbifold KZ connection we construct a functor from an affine parabolic category O of type A to the category O of a cyclotomic rational double affine Hecke algebra. We give several results concerning this functor.

We classify the irreducible unitary modules in category O for the rational Cherednik algebras of type G(r,1,n) and give explicit combinatorial formulas for their graded characters. More precisely, we produce a combinatorial algorithm…

We classify blocks of category $\mathcal{O}$ for rational Cherednik algebras and of cyclotomic Hecke algebras of type G(r,p,n) by using the "residue equivalence" for multi-partitions.

In this paper we discuss an analogue of the Kac-Weisfeiler conjecture for a certain class of almost commutative algebras. In particular, we prove the Kac-Weisfeiler type statement for rational Cherednik algebras.

The goal of this paper is to relate the quantum category $\mathcal{O}$ (known also as the category of modules over the mixed quantum group) at an odd root of unity to the affine Hecke category. Namely, we prove equivalences of highest…

The Razumov-Stroganov conjecture relates the ground-state coefficients in the even-length dense O(1) loop model to the enumeration of fully-packed loop configuration on the square, with alternating boundary conditions, refined according to…

We introduce the concept of a triangular decomposition for Banach and Fr\'echet-Stein algebras over $p$-adic fields, which allows us to define a category $\mathcal{O}$ for a wide array of topological algebras. In particular, we apply this…

We define and study cyclotomic quotients of affine Hecke algebras of type B. We establish an isomorphism between direct sums of blocks of these algebras and a generalisation, for type B, of cyclotomic quiver Hecke algebras which are a…

The goal of this paper is to lay the foundations for a combinatorial study, via orthogonal functions and intertwining operators, of category O for the rational Cherednik algebra of type G(r,p,n). As a first application, we give a…

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…

We undertake the study of complex rank analogues of parabolic category O defined using Deligne categories. We regard these categories as a family over an affine space, introduce a stratification on this parameter space, and formulate…

Let $\mathfrak{g}$ be a complex finite-dimensional semisimple Lie algebra and $\mathfrak{k}$ be any $\mathrm{sl}(2)$-subalgebra of $\mathfrak{g}$. In this paper we prove an earlier conjecture by Penkov and Zuckerman claiming that the first…

We prove that integral blocks of parabolic category O associated to the subalgebra gl(m) x gl(n) of gl(m+n) are Morita equivalent to quasi-hereditary covers of generalised Khovanov algebras. Although this result is in principle known, the…