Publications by Thomas Gerber | EPFL Graph Search

Duality and bicrystals on infinite binary matrices

The set of finite binary matrices of a given size is known to carry a finite type AA bicrystal structure. We first review this classical construction, explain how it yields a short proof of the equality between Kostka polynomials and one-dimensional sums t ...

2023

Generalised Howe duality and injectivity of induction: the symplectic case

Thomas Gerber

We study the symplectic Howe duality using two new and independent combinatorial methods: via determinantal formulae on the one hand, and via (bi)crystals on the other hand. The first approach allows us to establish a generalised version where weight multi ...

2022

A positive combinatorial formula for symplectic Kostka-Foulkes polynomials I: Rows

Thomas Gerber

We prove a conjecture of Lecouvey, which proposes a closed, positive combinatorial formula for symplectic Kostka-Foulkes polynomials, in the case of rows of arbitrary weight. To show this, we construct a new algorithm for computing cocyclage in terms of wh ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Generalized Mullineux Involution And Perverse Equivalences

Thomas Gerber

We define a generalization of the Mullineux involution on multipartitions using the theory of crystals for higher-level Fock spaces. Our generalized Mullineux involution turns up in representation theory via two important derived functors on cyclotomic Che ...

2020