Thomas Gerber

Research interests

My research is at the interface of representation theory and algebraic combinatorics. My favourites themes include:

Research papers

My research articles can also be found on arXiv and on HAL.

  1. Generalised core partitions and Diophantine equations
    With Olivier Brunat and Nathan Chapelier-Laget
    arXiv:2403.11191, 2024 [arXiv]
  2. Atomic length on Weyl groups
    With Nathan Chapelier-Laget
    To appear in Journal of Combinatorial Algebra, DOI 10.4171/JCA/104 [arXiv]
  3. Duality and bicrystals on infinite binary matrices
    With Cédric Lecouvey
    Annales de l'Institut Henri Poincaré D (Combinatorics, Physics and their Interactions) 10 (4) (2023) [arXiv, journal]
  4. Generalised Howe duality and injectivity of induction: the symplectic case
    With Jérémie Guilhot and Cédric Lecouvey
    Combinatorial Theory 2 (2) (2022), #12 [arXiv, journal]
  5. 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]
  6. Generalized Mullineux involution and perverse equivalences
    With Nicolas Jacon and Emily Norton
    Pacific Journal of Mathematics 306 (2020), N°2, 487-517 [arXiv, journal]
  7. Cylindric multipartitions and level-rank duality
    arXiv:1808.06087, 2018 [arXiv] (Notes not intended for publication)
  8. Heisenberg algebra, wedges and crystals
    Journal of Algebraic Combinatorics 49 (2019), 99-124 [arXiv, journal]
  9. The $sl_\infty $-crystal combinatorics of higher level Fock spaces
    With Emily Norton
    Journal of Combinatorial Algebra 2 (2018), 103-145 [arXiv, journal]
  10. Triple crystal action in Fock spaces
    Advances in Mathematics 329 (2018), 916-954 [arXiv, journal]
  11. Branching graphs for finite unitary groups in non-defining characteristic
    With Gerhard Hiss
    Communications in Algebra 45 (2016), 561-574 [arXiv, journal]
  12. 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]
  13. Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A
    Algebras and Representation Theory 18 (2015), 1009-1046 [arXiv, journal]
  14. Generalised canonical basic sets for Ariki-Koike algebras
    Journal of Algebra 413 (2014), 364-401 [arXiv, journal]

PhD thesis

Programming

I have written a few programs in Sage and GAP in the framework of my research, notably for:

Don't hesitate to write me for any particular request.