6 papers
Representations and characters of quantum affine algebras at the crossroads between cluster categorification and quantum integrable models
David Hernandez
In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and relat…
Jordan-Hölder property for shifted quantum affine algebras
David Hernandez, Huafeng Zhang
We prove that finite length representations of shifted quantum affine algebras in category are stable by fusion product. This implies that in the topolo…
Symmetries of Grothendieck rings in representation theory
David Hernandez
This is a written version of the invited lecture at the 9th European Congress of Mathematics in July 2024 in Sevilla. We review certain new symmetries of Grothendieck rings that ha…
Monoidal Jantzen filtrations
Ryo Fujita, David Hernandez
We introduce a monoidal analogue of Jantzen filtrations in the framework of monoidal abelian categories with generic braidings. It leads to a deformation of the multiplication of t…
Representations of shifted quantum affine algebras and cluster algebras I. The simply-laced case
Christof Geiss, David Hernandez, Bernard Leclerc
We introduce a family of cluster algebras of infinite rank associated with root systems of type , , . We show that suitable completions of these cluster algebras are isomo…
Generalized Green functions and unipotent classes for finite reductive groups, I
Toshiaki Shoji
The algorithm of computing generalized Green functions of a finite reductive group contains some unkonwn scalars occuring from the F_q structure of irreducible local systems on uni…