8 citations · 26 across the 13 of their papers we have counts for
17 papers
Enumerating cores of charged multipartitions
Thomas Gerber, Emily Norton
Granville and Ono proved that there is an -core partition of for every if and only if , which translates to a statement about the existence of defe…
Quantized Howe-type dualities via Koornwinder polynomials and the X=K phenomenon
Thomas Gerber, Bogdan Ion, Cédric Lecouvey +1
We derive the equality between one-dimensional sums associated with tensor products of Kirillov-Reshetikhin column crystals of classical affine types and Lusztig q-analogues of wei…
Entropy of affine permutations and universality of affine atomic lengths
Nathan Chapelier-Laget, Thomas Gerber, Nicolas Jacon +1
We introduce and study the notion of entropy of affine permutations and prove that it coincides with the atomic length associated with the sum of the fundamental weights for a type…
Generalised core partitions and Diophantine equations
Olivier Brunat, Nathan Chapelier-Laget, Thomas Gerber
We study generalised core partitions arising from affine Grassmannian elements in arbitrary Dynkin type. The corresponding notion of size is given by the atomic length in the sense…
Atomic length on Weyl groups
Nathan Chapelier-Laget, Thomas Gerber
We define a new statistic on Weyl groups called the atomic length and investigate its combinatorial and representation-theoretic properties. In finite types, we show a number of pr…
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…