My area of research is algebraic combinatorics. More precisely, I investigate the combinatorial aspects in modular representation theory of reflection groups (and of their associated Hecke algebras), and of finite classical groups. I am in particular interested in the connections with quantum groups, via the theory of crystals and canonical bases. Insofar as possible, I like to use methods from combinatorics on words.
𝔰𝔩∞-crystal combinatorics of higher level Fock spaces. With Emily Norton.
Heisenberg algebra, wedges and crystals.
Triple crystal action in Fock spaces.
Branching graphs for finite unitary groups in non-defining characteristic.
Comm. Algebra 45 (2016), 561-574
Harish-Chandra series in finite unitary groups and crystal graphs.
Gerhard Hiss and
International Mathematics Research Notices 22 (2015), 12206-12250.
Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A.
Algebras and Representation Theory 18 (2015), 1009-1046.
Generalised canonical basic sets for Ariki-Koike algebras.
Journal of Algebra 413 (2014), 364-401.
Decomposition matrices for Ariki-Koike algebras and crystal isomorphisms in Fock spaces (available here).
Directed by Cédric Lecouvey and Nicolas Jacon, defended on July 1st, 2014.
Some beamer talks
- Ariki's theorem, for ARTY 2 (Erlangen, 8-10 June 2014).
- An analogue of the bumping algorithm in affine type A, for the 72nd Séminaire Lotharingien de Combinatoire (Lyon, 24 March 2014).
- Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A, for the Nikolaus conference (Aachen, 7 December 2013).
- Decomposition matrices of Ariki-Koike algebras, for YRRT (Wuppertal, 7 October 2013) [picture!] and ARTY (Erlangen, 27 May 2013).
- Représentations du groupe symétrique, for the "Journée des Doctorants" (Blois, October 2012).