Abstract
We consider simple modules for a Hecke algebra with a parameter of quantum characteristic e. Equivalently, we consider simple modules D^{λ}, labelled by erestricted partitions λ of n, for a cyclotomic KLR algebra R^{Λ0}_{n}R_{n}^{Λ0} over a field of characteristic p ≥ 0, with mild restrictions on p. If all parts of λ are at most 2, we identify a set DStd_{e},_{p}(λ) of standard λtableaux, which is defined combinatorially and naturally labels a basis of Dλ. In particular, we prove that the qcharacter of D^{λ} can be described in terms of DStd_{e},_{p}(λ). We show that a certain natural approach to constructing a basis of an arbitrary D^{λ} does not work in general, giving a counterexample to a conjecture of Mathas.
Original language  English 

Pages (fromto)  631–669 
Number of pages  39 
Journal  Transformation Groups 
Volume  23 
Issue number  3 
Early online date  19 Oct 2017 
DOIs  
Publication status  Published  Sep 2018 
Profiles

Sinead Lyle
 School of Engineering, Mathematics and Physics  Associate Professor
 Algebra and Combinatorics  Member
Person: Research Group Member, Academic, Teaching & Research