• Corpus ID: 222133854

KLR and Schur algebras for curves and semi-cuspidal representations.

  title={KLR and Schur algebras for curves and semi-cuspidal representations.},
  author={Ruslan Maksimau and Alexandre Minets},
  journal={arXiv: Representation Theory},
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 affinized symmetric algebras. When $C=\mathbb P^1$, a version of curve Schur algebra turns out to be Morita equivalent to the imaginary semi-cuspidal category of the Kronecker quiver in any characteristic. As a consequence, we argue that one should not expect to have… 


Quiver Schur algebras and cohomological Hall algebras
We establish a connection between a generalization of KLR algebras, called quiver Schur algebras, and the cohomological Hall algebras of Kontsevich and Soibelman. More specifically, we realize quiver
Quiver Hecke Algebras and 2-Lie Algebras
We provide an introduction to the 2-representation theory of Kac-Moody algebras, starting with basic properties of nil Hecke algebras and quiver Hecke algebras, and continuing with the resulting
Principal G bundles over elliptic curves
Let $G$ be a simple and simply connected complex Lie group. We discuss the moduli space of holomorphic semistable principal $G$ bundles over an elliptic curve $E$. In particular we give a new proof
Affine zigzag algebras and imaginary strata for KLR algebras
KLR algebras of affine ADE \texttt {ADE} types are known to be properly stratified if the characteristic of the ground field is greater than some explicit bound. Understanding the
Elliptic Springer theory
We introduce an elliptic version of the Grothendieck–Springer sheaf and establish elliptic analogues of the basic results of Springer theory. From a geometric perspective, our constructions
Imaginary Schur-Weyl duality
We study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define
The elliptic Hall algebra and the equivariant K-theory of the Hilbert scheme of $\mathbb{A}^2$
In this paper we compute the convolution algebra in the equivariant K-theory of the Hilbert scheme of A^2. We show that it is isomorphic to the elliptic Hall algebra, and hence to the spherical DAHA
Geometric Satake, Springer correspondence, and small representations II
For a split reductive group scheme $G$ over a commutative ring $k$ with Weyl group $W$, there is an important functor $Rep(G,k) \to Rep(W,k)$ defined by taking the zero weight space. We prove that
Torsion and Abelianization in Equivariant Cohomology
Let X be a topological space upon which a compact connected Lie group G acts. It is well known that the equivariant cohomology H*G (X; Q) is isomorphic to the subalgebra of Weyl group invariants of
Flag versions of quiver Grassmannians for Dynkin quivers have no odd cohomology over Z
We prove that flag versions of quiver Grassmannians (also knows as Lusztig’s fibers) for Dynkin quivers (types A, D, E) have no odd cohomology over Z. Moreover, for types A and D we prove that these