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math.CO2021
Generalised Howe dualityand injectivity of induction: the symplectic case
Thomas Gerber, Jeremie Guilhot, Cédric Lecouvey
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 fi…
math.CO2020
Duality and bicrystals on infinite binary matrices
Thomas Gerber, Cédric Lecouvey
The set of finite binary matrices of a given size is known to carry a finite type A bicrystal structure. We first review this classical construction, explain how it yields a short…
math.CO2019
A positive combinatorial formula for symplectic Kostka-Foulkes polynomials I: Rows
Maciej Dołęga, Thomas Gerber, Jacinta Torres
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 sh…