Computational Algebra Seminar: Mathas -- Computing decomposition numbers of symmetric groups

Speaker: Andrew Mathas (Sydney)  
Title: Computing decomposition numbers of symmetric groups  
Time & Place: 15.00-16.00, Thursday 14 May, SMRI Seminar Rm
Abstract: I will describe an algorithm for computing decomposition numbers of the 
symmetric groups over finite fields. The approach is based on Young's seminormal form 
from the semisimple representation theory of the symmetric groups, but cast in very 
different clothes from the non-semisimple representation theory of cyclotomic KLR 
algebras. These algebras include the group algebras of the symmetric groups as a special 
case. Computationally, the advantages are that we can use the speed of the semisimple 
representation theory combined with idempotent truncation to compute Gram matrices on 
significantly spaces than are accessible using classical approaches. The resulting code 
works for cyclotomic KLR algebras of affine type A or C of arbitrary dominant weight. 
If time permits, I will discuss a large family of very explicit and "relatively small" 
counterexamples to the James conjecture that were found this way.