8 citations · 26 across the 13 of their papers we have counts for
13 papers · 1 filter
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…
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…
Cylindric multipartitions and level-rank duality
Thomas Gerber
We show that a multipartition is cylindric if and only if its level rank-dual is a source in the corresponding affine type crystal. This provides an algebraic interpretation of…
Generalized Mullineux involution and perverse equivalences
Thomas Gerber, Nicolas Jacon, Emily Norton
We define a generalization of the Mullineux involution on multipartitions using the theory of crystals for higher level Fock spaces. Our generalized Mullineux involution turns up i…
The -crystal combinatorics of higher level Fock spaces
Thomas Gerber, Emily Norton
For integers , the level Fock space has an -crystal structure arising from the action of a Heisenberg algebra, intertwining the $\widehat…
Heisenberg algebra, wedges and crystals
Thomas Gerber
We explain how the action of the Heisenberg algebra on the space of q-deformed wedges yields the Heisenberg crystal structure on charged multipartitions, by using the boson-fermion…
Triple crystal action in Fock spaces
Thomas Gerber
We make explicit a triple crystal structure on higher level Fock spaces, by investigating at the combinatorial level the actions of two affine quantum groups and of a Heisenberg al…
Branching graphs for finite unitary groups in non-defining characteristic
Thomas Gerber, Gerhard Hiss
We show that the modular branching rule (in the sense of Harish-Chandra) on unipotent modules for finite unitary groups is piecewise described by particular connected components of…
Harish-Chandra series in finite unitary groups and crystal graphs
Thomas Gerber, Gerhard Hiss, Nicolas Jacon
The distribution of the unipotent modules (in non-defining prime characteristic) of the finite unitary groups into Harish-Chandra series is investigated. We formulate a series of c…
Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A
Thomas Gerber
We are interested in the structure of the crystal graph of level Fock spaces representations of . Since the work of Shan [26], we kno…
Generalised canonical basic sets for Ariki-Koike algebras
Thomas Gerber
Let H be a non semi-simple Ariki-Koike algebra. According to [18] and [14], there is a generalisation of Lusztig's a-function which induces a natural order (parametrised by a tuple…