On symmetric quotients of symmetric algebras

18 October 2013
Radha Kessar
We investigate symmetric quotient algebras of symmetric algebras, with an emphasis on finite group algebras over a complete discrete valuation ring R with residue field of positive characteristic p. Using elementary methods, we show that if an ordinary irreducible character of a finite group gives rise to a symmetric quotient over R which is not a matrix algebra, then the decomposition numbers of the row labelled by the character are all divisible by p. In a different direction, we show that if is P is a finite p-group with a cyclic normal subgroup of index p, then every ordinary irreducible character of P gives rise to a symmetric quotient of RP. This is joint work with Shigeo Koshitani and Markus Linckelmann.
  • Representation Theory Seminar