Quiver Schur algebras and Koszul duality
Ruslan Maksimau
Abstract
We prove that the category of graded finitely generated representations of the the cyclotomic quiver Schur algebra is a Koszul category.
Table of Contents
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Quiver Schur algebras and Koszul duality
Authors
Ruslan Maksimau
Abstract
We prove that the category of graded finitely generated representations of the the cyclotomic quiver Schur algebra is a Koszul category.
Paper Structure
This paper contains 28 sections, 55 theorems, 86 equations.
Table of Contents
- Introduction
- Quiver Schur algebras and Koszul duality
- Graded categories
- Koszul duality
- Graded highest weight categories
- Combinatorics
- Rigid modules
- Cyclotomic Hecke and $q$-Schur algebra
- Cyclotomic KLR-algebra
- Quiver Schur algebra
- Admissible gradings
- Quiver Schur grading is admissible
- Lie algebras
- Category $\mathbf{A}$
- The Koszul grading
- ...and 13 more sections
Key Result
Theorem 1.1
There exists a graded algebra isomorphism $^bS_{\mathbf{d}}^{\mathbf{s}}\simeq S^\mathcal{O}$. ∎
Theorems & Definitions (121)
- Theorem 1.1
- Definition 2.1
- Definition 2.2
- Definition 2.3
- Definition 2.4
- Theorem 2.5
- Corollary 2.6
- Definition 2.7
- Lemma 2.8
- proof
- ...and 111 more