Related papers: Imaginary Schur-Weyl duality
From a certain induced representation $\mathcal{P}_\ell$ of a double affine Weyl group, we construct a ring $\mathcal{F}_\ell$ that is isomorphic to the fusion ring, or Verlinde algebra, associated to affine Lie algebras at fixed positive…
We study the representation theory of the Bershadsky-Polyakov algebra $\mathcal W_k = \mathcal{W}_k(sl_3,f_{\theta})$. In particular, Zhu algebra of $\mathcal W_k$ is isomorphic to a certain quotient of the Smith algebra, after changing the…
We study the super analogue of the Molev-Ragoucy reflection algebras, which we call twisted super Yangians of type AIII, and classify their finite-dimensional irreducible representations under certain conditions. These superalgebras are…
This is a survey paper about affine Hecke algebras. We start from scratch and discuss some algebraic aspects of their representation theory, referring to the literature for proofs. We aim in particular at the classification of irreducible…
We establish the Schur-Weyl type duality between double affine Hecke algebras and quantum toroidal superalgebras, generalizing the well known result of Vasserot-Varagnolo [VV96] to the super case.
In this paper we classify and give Kazhdan-Lusztig type character formulas for equivariantly irreducible representations of Lie algebras of reductive algebraic groups over a field of large positive characteristic. The equivariance is with…
We construct new irreducible weight modules over quantum affine algebras of type I with all weight spaces infinite-dimensional. These modules are obtained by parabolic induction from irreducible modules over the Heisenberg subalgebra.
Irreducible representations are the building blocks of general, semisimple Galois representations \rho, and cuspidal representations are the building blocks of automorphic forms \pi of the general linear group. It is expected that when an…
The irreducible integrable representations with finite-dimensional weight spaces of toroidal Lie algebras on which the center acts non-trivially were classified by S.Eswara Rao. In this paper we give a compact proof of the results that lead…
We first define the notion of good filtration dimension and Weyl filtration dimension in a quasi-hereditary algebra. We calculate these dimensions explicitly for all irreducible modules in SL_2 and SL_3. We use these to show that the global…
In the first part of this series, the authors introduced the quantum wreath product, providing a unified framework that encompasses numerous results previously addressed only through case-by-case analysis. This paper shifts focus to the…
We develop a general technique of constructing new irreducible weight modules for any affine Kac-Moody algebra using the parabolic induction, in the case when the Levi factor of a parabolic subalgebra is infinite-dimensional and the central…
The rook monoid, also known as the symmetric inverse monoid, is the archetypal structure when it comes to extend the principle of symmetry. In this paper, we establish a Schur-Weyl duality between this monoid and an extension of the…
One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra [K]. A Lie pseudoalgebra is a generalization of the…
In this paper, we characterize quasi-integrable modules, of nonzero level, over twisted affine Lie superalgebras. We show that quasi-integrable modules are not necessarily highest weight modules. We prove that each quasi-integrable module…
The polynomial ideals studied by A. Garsia and C. Procesi play an important role in the theory of Kostka polynomials. We give multiparameter flat deformations of these ideals and define an action of the extended affine symmetric group on…
Let $V$ be a free module of rank $n$ over a commutative unital ring $k$. We prove that tensor space $V^{\otimes r}$ satisfies Schur--Weyl duality, regarded as a bimodule for the action of the group algebra of the Weyl group of…
We construct a bijection between admissible representations for an affine Lie algebra $\mathfrak{g}$ at boundary admissible levels and $\mathbb{C}^\times$ fixed points in homogeneous elliptic affine Springer fibres for the Langlands dual…
Given a smooth curve $C$, we define and study analogues of KLR algebras and quiver Schur algebras, where quiver representations are replaced by torsion sheaves on $C$. In particular, they provide a geometric realization for certain…
In this paper, we study the irreducible objects of the category Cf in of integrable representations for Map full Toroidal Lie algebras with finite dimensional weight spaces. These representations turn out to be single point evaluation…