Fusion rings for quantum groups
type: Item
instance of: scholarly article
title: Fusion rings for quantum groups
zbMATH Open document ID: 1322.17007
author: Henning Haahr Andersen
author: Catharina Stroppel
published in: Algebras and Representation Theory
publication date: 2015-01-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/1212.5736
review text: In this paper the authors use tilting modules to study fusion rings for quantum groups at complex roots of unity. In all types, the authors provide an easy method to realize the fusion ring as a quotient of a polynomial ring, in particular, giving an explicit description for generators of the fusion ideal. In types \(A\) and \(C\) this even gives a minimal set of generators, while in other types the situation is more complicated in general. The paper uses crucially the representation theory and combinatorics of affine Weyl groups.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 20G42
zbMATH DE Number: 6384244
zbMATH Keywords: fusion ring
zbMATH Keywords: quantum group
zbMATH Keywords: tilting module
zbMATH Keywords: root of unity
MaRDI profile type: Publication
OpenAlex ID: W2106446599
arXiv ID: 1212.5736
cites work: Tensor products of quantized tilting modules
cites work: Fusion categories arising from semisimple Lie algebras
cites work: Representations of quantum algebras
cites work: Q3941610
cites work: PRESENTATIONS OF WESS–ZUMINO–WITTEN FUSION RINGS
cites work: A conjectural presentation of fusion algebras
cites work: On tilting modules for algebraic groups
cites work: Fusion rings of loop group representations
cites work: Q4002278
cites work: Lattice path proofs for determinantal formulas for symplectic and orthogonal characters
cites work: Q4015547
cites work: The \(\widehat {\mathfrak {sl}}(n)_k\)-WZNW fusion ring: a combinatorial construction and a realisation as quotient of quantum cohomology
cites work: A generalization of the Littlewood-Richardson rule
cites work: Quantum groups at roots of 1
cites work: Introduction to quantum groups
cites work: The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences
cites work: A q-Analogue of Kempf's vanishing theorem
cites work: The subcomodule structure of the quantum symmetric powers
DOI: 10.1007/S10468-014-9479-6
description: scientific article