On the classification of simple modules for cyclotomic Hecke algebras of type G(m,1,n) and Kleshchev multipartitions

We give a proof of a conjecture that Kleshchev multipartitions are those partitions which parametrize non-zero simple modules obtained as factor modules of Specht modules by their own radicals.Comment: 11 pages, LaTeX, the last theorem and related preparatory results are remove

Proof of the modular branching rule for cyclotomic Hecke algebras

We prove the modular branching rule of the cyclotomic Hecke algebras, which has remained open.Comment: 9 pages, last section removed, (v3,v4) minor changes in the introduction, (v5,v6) more detailed citations added, typos correcte

Some remarks on A_1^{(1)} soliton cellular automata

In this short note, we describe the A_1^{(1)} soliton cellular automata as an evolution of a poset. This allows us to explain the conservation laws for the A_1^{(1)} soliton cellular automata, one given by Torii, Takahashi and Satsuma, and the other given by Fukuda, Okado and Yamada, in terms of the stack permutations of states in a very natural manner. As a biproduct, we can prove a conjectured formula relating these laws.Comment: 10 pages, LaTeX2

An LLT-type algorithm for computing higher-level canonical bases

We give a fast algorithm for computing the canonical basis of an irreducible highest-weight module for $U_q(\hat{\mathfrak{sl}}_e)$, generalising the LLT algorithm

Dipper-James-Murphy's conjecture for Hecke algebras of type B

We prove a conjecture by Dipper, James and Murphy that a bipartition is restricted if and only if it is Kleshchev. Hence the restricted bipartitions naturally label the crystal graphs of level two irreducible integrable $\mathcal{U}_v({\hat{\mathfrak{sl}}_e})$-modules and the simple modules of Hecke algebras of type $B_n$.Comment: The revised version corrects minor points, the proof of lemma 3.3 has been improve