相关论文: Suzuki functor at the critical level

In this paper we introduce a generalization of the Nakayama functor for finite-dimensional algebras. This is obtained by abstracting its interaction with the forgetful functor to vector spaces. In particular, we characterize the Nakayama…

For any module over the affine Weyl group we construct a representation of the associated trigonometric Cherednik algebra $A(k)$ at critical level in terms of Dunkl type operators. Under this representation the center of $A(k)$ produces…

Let $\CC^0_{\g}$ be the category of finite-dimensional integrable modules over the quantum affine algebra $U_{q}'(\g)$ and let $R^{A_\infty}\gmod$ denote the category of finite-dimensional graded modules over the quiver Hecke algebra of…

The representation theory of rational Cherednik algebras of type A at t=0 gives rise, by considering supports, to a natural family of smooth Lagrangian subvarieties of the Calogero-Moser space. The goal of this article is to make precise…

A combinatorial formula for Pfaffian for the universal enveloping algebra of the affine Kac - Moody algebra of even orthogonal Lie algebra is proved. It allows easily to compute the image of this Segal-Sugawara vector under the…

In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we…

In this article we study rational Cherednik algebras at $t = 1$ in positive characteristic. We study a finite dimensional quotient of the rational Cherednik algebra called the restricted rational Cherednik algebra. When the corresponding…

Important connections in representation theory arise from resolving a finite-dimensional algebra by an endomorphism algebra of a generator-cogenerator with finite global dimension; for instance, Auslander's correspondence, classical…

Let $\mathfrak{g}(A)$ be the Kac-Moody algebra with respect to a symmetrizable generalized Cartan matrix $A$. We give an explicit presentation of the fix-point Lie subalgebra $\mathfrak{k}(A)$ of $\mathfrak{g}(A)$ with respect to the…

In this paper, we present an integral Suzuki-type fixed point theorem for multivalued mappings defined on a complete metric space in terms of the \'{C}iri\'{c} integral contractions. As an application, we will prove an existence and…

Arakawa, Suzuki and Tsuchiya constructed a correspondence between certain modules of the trigonometric Cherednik algebra $\mathfrak{C}_N$ depending on a parameter $\kappa\in\mathbb{C}$, and certain modules of the affine Lie algebra…

We define an extension of the affine Brauer algebra, the type B/C affine Brauer algebra. This new algebra contains the hyperoctahedral group and it naturally acts on $END_K(X \otimes V^{\otimes k})$ for Orthogonal and Symplectic groups.…

This paper introduces calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The primary technique is to provide indexing sets for controlling the…

We discuss tilting modules of affine quasi-hereditary algebras. We present an existence theorem of indecomposable tilting modules when the algebra has a large center and use it to deduce a criterion for an exact functor between two affine…

The Feigin--Frenkel theorem states that, over the complex numbers, the centre of the universal affine vertex algebra at the critical level is an infinite rank polynomial algebra. The first author and W.~Wang observed that in positive…

Let $\mathcal K$ be a complete quasivariety of completely regular universal topological algebras of continuous signature $\mathcal E$ (which means that $\mathcal K$ is closed under taking subalgebras, Cartesian products, and includes all…

We give explicit formulas for the elements of the center of the completed quantum affine algebra in type $A$ at the critical level which are associated with the fundamental representations. We calculate the images of these elements under a…

We describe Serre functors for (generalisations of) the category O associated with a semi-simple complex Lie algebra. In our approach, projective-injective modules play an important role. They control the Serre functor in the case of a…

In this paper we prove a general result saying that under certain hypothesis an embedding of an affine vertex algebra into an affine $W$--algebra is conformal if and only if their central charges coincide. This result extends our previous…

Basic properties of symplectic reflection algebras over an algebraically closed field k of positive characteristic are laid out. These algebras are always finite modules over their centres, in contrast to the situation in characteristic 0.…