Representations of wreath products of algebras

Abstract

This is the unspecified version of the paper.This version of the publication may differ from the final published version. Permanent

Filtrations in Rouquier Blocks of Symmetric Groups and Schur Algebras

“…General theory. We introduce standard constructions of modules for wreath products of algebras (see, e.g., [4]). Suppose R ∈ {K, O, k} and let Γ be an R-algebra, free and of finite rank as an R-module.…”

“…We have the following formulas for analogous polynomials describing the radical series of P(λ), Ω(λ), Y(λ) and S(λ), using results obtained in [4]. Theorem 6.1.…”

“…These are derived from general formulas for filtrations of modules for wreath products presented in [4]. We end by giving positive answers to special cases of some conjectures.…”

“…The formulas for rad Ω,λ,µ (v) and rad P,λ,µ (v) are obtained in [4, Proposition 7.1]. The formulas for rad S,λ,σ (v) and rad Y,λ,σ (v) can be obtained in an entirely similar manner, and by comparing with the formulas obtained for rad Ω,λ,σ (v) and rad P,λ,σ (v), we get the desired presentations.…”

Some Canonical Basis Vectors in the Basic Uq([formula]n)-Module

“…As predicted by Rouquier in 1992 (see [11]), one can prove Broué's conjecture for certain blocks of the symmetric groups by showing that they are Morita equivalent to blocks of wreath products of symmetric groups [2]. These wreath products are analyzed in [3] and applied to the study of blocks of symmetric groups in [4]. They are the source of the formula we present here.…”