Abstract
Let ℋ = ℋℂ, −1(𝔖 n ) be the Hecke algebra of the symmetric group 𝔖 n . For partitions λ and ν with ν 2 − regular, define the Specht module S(λ) and the irreducible module D(ν). Define d λν = [S(λ): D(ν)] to be the composition multiplicity of D(ν) in S(λ). In this paper we compute the decomposition numbers d λν for all partitions of the form λ = (a, c, 1 b ) and ν 2 − regular.
2010 Mathematics Subject Classification:
ACKNOWLEDGMENT
I would like to thank my supervisor Dr. Sinéad Lyle who brought this subject to my attention for her great help and advices. Also, I would like to thank the ministry of higher education in Saudi Arabia for granting me a scholarship to study a PhD degree in the UK. I would also like to thank the referee for their careful reading of this paper and constructive comments.
Notes
Communicated by K. Misra.