Symmetric quotients of symmetric algebras
Radha Kessar, Shigeo Koshitani and Markus Linckelmann

Abstract. We investigate symmetric quotient algebras of symmetric algebras, with an emphasis 
on finite group algebras over a complete discrete valuation ring O. Using elementary methods, 
we show that if an ordinary irreducible character # of a finite group G gives rise to a symmetric 
quotient over O which is not a matrix algebra, then the decomposition numbers of the row 
labelled by # are all divisible by the characteristic p of the residue field of O.