A Specht filtration of permutation modules over KLR algebras

Source abstract

Abstract Kleshchev–Mathas–Ram give a presentation of the Specht module $$S^\lambda$$ S λ as a quotient of the permutation module $$M^\lambda$$ M λ . In this paper, we construct a (graded) Specht filtration of the permutation module $$M^\lambda$$ M λ in the following cases: when $$\lambda = (k,1^r)$$ λ = ( k , 1 r ) is a hook partition, over the KLR algebra of type $$A^{(1)}_{e-1}$$ A e - 1 ( 1 ) for $$e > 2$$ e > 2 ; and when $$\lambda = (k,r)$$ λ = ( k , r ) is a two-row partition with $$k \ge r$$ k ≥ r , over the KLR algebra of type $$A_\infty$$ A ∞ . Furthermore, when $$\lambda$$ λ is an arbitrary partition in type $$A_\infty$$ A ∞ , we construct a filtration of $$M^\lambda$$ M λ such that each subquotient $$M_i / M_{i+1}$$ M i / M i + 1 admits a Specht resolution.