Research interests
My research is at the interface of representation theory and algebraic combinatorics. My favourites themes include:
- modular representation theory of finite groups, representations of Hecke algebras and Cherednik algebras, categorification,
- Coxeter groups and root systems combinatorics,
- symmetric polynomials,
- Lie algebras, Kac-Moody algebras, quantum groups and their representations, crystals and canonical bases,
- interactions with probability theory.
Research papers
My research articles can also be found on arXiv and on HAL.
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Generalised core partitions and Diophantine equations
With Olivier Brunat and Nathan Chapelier-Laget
arXiv:2403.11191, 2024 [arXiv] -
Atomic length in Weyl groups
With Nathan Chapelier-Laget
arXiv:2211.12359, 2022 [arXiv] -
Duality and bicrystals on infinite binary matrices
With Cédric Lecouvey
Annales de l'Institut Henri Poincaré D (Combinatorics, Physics and their Interactions), DOI 10.4171/AIHPD/165, 2023 [arXiv, journal] -
Generalised Howe duality and injectivity of induction: the symplectic case
With Jérémie Guilhot and Cédric Lecouvey
Combinatorial Theory 2 (2) (2022), #12 [arXiv, journal] -
A positive combinatorial formula for symplectic Kostka-Foulkes polynomials I: Rows
With Maciej Dołęga and Jacinta Torres
Journal of Algebra 560 (2020), 1253-1296 [arXiv, journal] -
Generalized Mullineux involution and perverse equivalences
With Nicolas Jacon and Emily Norton
Pacific Journal of Mathematics 306 (2020), N°2, 487-517 [arXiv, journal] -
Cylindric multipartitions and level-rank duality
arXiv:1808.06087, 2018 [arXiv] -
Heisenberg algebra, wedges and crystals
Journal of Algebraic Combinatorics 49 (2019), 99-124 [arXiv, journal] -
The $sl_\infty $-crystal combinatorics of higher level Fock spaces
With Emily Norton
Journal of Combinatorial Algebra 2 (2018), 103-145 [arXiv, journal] -
Triple crystal action in Fock spaces
Advances in Mathematics 329 (2018), 916-954 [arXiv, journal] -
Branching graphs for finite unitary groups in non-defining characteristic
With Gerhard Hiss
Communications in Algebra 45 (2016), 561-574 [arXiv, journal] -
Harish-Chandra series in finite unitary groups and crystal graphs
With Gerhard Hiss and Nicolas Jacon
International Mathematics Research Notices 22 (2015), 12206-12250 [arXiv, journal] -
Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A
Algebras and Representation Theory 18 (2015), 1009-1046 [arXiv, journal] -
Generalised canonical basic sets for Ariki-Koike algebras
Journal of Algebra 413 (2014), 364-401 [arXiv, journal]
PhD thesis
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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.
Programming
I have written a few programs in Sage and GAP in the framework of my research, notably for:
- computing affine type A crystals (realisation by multipartitions) and certain crystal isomorphisms,
- computing the Heisenberg crystal and the generalised Mullineux involution,
- implementing the atomic length on Weyl groups.