Related papers: Linear Koszul duality and affine Hecke algebras
For a pair of affine toric varieties X and Y defined by dual cones, we define an equivalence between two triangulated categories. The first is a mixed version of the equivariant derived category of X and the second is a mixed version of the…
Affine Hecke algebras arise naturally in the study of smooth representations of reductive $p$-adic groups. Finite dimensional complex representations of affine Hecke algebras (under some restriction on the isogeny class and the parameter…
After establishing a geometric Schur-Weyl duality in a general setting, we recall this duality in type A in the finite and affine case. We extend the duality in the affine case to positive parts of the affine algebras. The positive parts…
Let $g$ be a reductive Lie algebra over a field of characteristic zero. Suppose $g$ acts on a complex of vector spaces $M$ by $i_\lambda$ and $L_\lambda$, which satisfy the identities as contraction and Lie derivative do for smooth…
Motivated by a result from string topology, we prove a duality in topological Hochschild homology (THH). The duality relates the THH of an E_1-algebra spectrum and the THH of its derived Koszul dual algebra under certain compactness…
In this article, we introduce basic aspects of the algebraic notion of Koszul duality for a physics audience. We then review its appearance in the physical problem of coupling QFTs to topological line defects, and illustrate the concept…
This paper presents a $q$-analogue of an extension of the tensor algebra given by the same author. This new algebra naturally contains the ordinary tensor algebra and the Iwahori-Hecke algebra type $A$ of infinite degree. Namely this…
This paper gives the classification of the Whittaker unitary dual for affine graded Hecke algebras of type E. By the Iwahori-Matsumoto involution, this is equivalent also to the classification of the spherical unitary dual for type E. This…
There are two natural analogues of algebraic foliations in derived algebraic geometry, called partition Lie algebroids and infinitesimal derived foliations, and both make sense in general characteristics. We construct an equivalence between…
We develop algebraic and geometrical approaches toward canonical bases for affine q-Schur algebras of arbitrary type introduced in this paper. A duality between an affine q-Schur algebra and a corresponding affine Hecke algebra is…
Koszul algebras have arisen in many contexts; algebraic geometry, combinatorics, Lie algebras, non-commutative geometry and topology. The aim of this paper and several sequel papers is to show that for any finite dimensional algebra there…
In this paper, we introduce a new notion of algebra over a linear $\infty$-operad and a corresponding notion of coalgebra over an $\infty$-cooperad. We next extend the Koszul duality between linear $\infty$-operads and linear…
In this paper we prove a version of curved Koszul duality for Z/2Z-graded curved coalgebras and their coBar differential graded algebras. A curved version of the homological perturbation lemma is also obtained as a useful technical tool for…
We prove that the category of graded finitely generated representations of the the cyclotomic quiver Schur algebra is a Koszul category.
We define the formal affine Demazure algebra and formal affine Hecke algebra associated to a Kac-Moody root system. We prove the structure theorems of these algebras, hence, extending several result and construction (presentation in terms…
We study the Koszul duality between augmented $E_n$-algebras and augmented $E_n$-coalgebras in a symmetric monoidal stable infinity $1$-category equipped with a filtration in a suitable sense. We obtain that the Koszul duality constructions…
We study the curved Koszul duality theory for associative algebras presented by quadratic-linear-constant (QLC) relations. As an application, we investigate the cyclic (co)homology of a QLC algebra and its Koszul dual curved DG algebra, and…
We study a class of representations called ``calibrated representations'' of the degenerate double affine Hecke algebra and those of the rational Cherednik algebra of type ${\mathrm{GL}}_n$. We give a realization of calibrated irreducible…
Feigin-Frenkel duality is the isomorphism between the principal $\mathcal{W}$-algebras of a simple Lie algebra $\mathfrak{g}$ and its Langlands dual Lie algebra ${}^L\mathfrak{g}$. A generalization of this duality to a larger family of…
We construct an equivalence of $E_{2}$ algebras between two models for the Thom spectrum of the free loop space that are related by derived Koszul duality. To do this, we describe the functoriality and invariance properties of topological…