Innovating Works

QAffine

Financiado
Representations of quantum affine algebras and applications
Quantum affine algebras are important examples of Drinfeld-Jimbo quantum groups. They can be defined as quantizations of affine Kac-Moody algebras or as affinizations of finite type quantum groups (Drinfeld Theorem). The represent... Quantum affine algebras are important examples of Drinfeld-Jimbo quantum groups. They can be defined as quantizations of affine Kac-Moody algebras or as affinizations of finite type quantum groups (Drinfeld Theorem). The representation theory of quantum affine algebras is very rich. It has been studied intensively during the past twenty five years from different point of views, in particular in connections with various fields in mathematics and in physics, such as geometry (geometric representation theory, geometric Langlands program), topology (invariants in small dimension), combinatorics (crystals, positivity problems) and theoretical physics (Bethe Ansatz, integrable systems). In particular, the category C of finite-dimensional representations of a quantum affine algebra is one of the most studied object in quantum groups theory. However, many important and fundamental questions are still unsolved in this field. The aim of the research project is to make significant advances in the understanding of the category C as well as of its applications in the following five directions. They seem to us to be the most promising directions for this field in the next years : 1. Asymptotical representations and applications to quantum integrable systems, 2. G-bundles on elliptic curves and quantum groups at roots of 1, 3. Categorications (of cluster algebras and of quantum groups), 4. Langlands duality for quantum groups, 5. Proof of (geometric) character formulas and applications. The resources would be used for the following : (1) Hiring of 2 PhD students (in 2015 and 2017). (2) Hiring of 2 Postdocs (in 2015 and 2017). (3) Invitations and travel for ongoing and future scientific collaborations. (4) Organization of a summer school in Paris on quantum affine algebras. ver más
28/02/2021
CNRS
1M€
Perfil tecnológico estimado
Duración del proyecto: 67 meses Fecha Inicio: 2015-07-23
Fecha Fin: 2021-02-28

Línea de financiación: concedida

El organismo H2020 notifico la concesión del proyecto el día 2021-02-28
Línea de financiación objetivo El proyecto se financió a través de la siguiente ayuda:
ERC-CoG-2014: ERC Consolidator Grant
Cerrada hace 10 años
Presupuesto El presupuesto total del proyecto asciende a 1M€
Líder del proyecto
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE... No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico TRL 4-5