The Partition Algebra as a Centralizer Algebra of the Alternating Group

ABSTRACT

In this article, we focus on the result of V.F.R. Jones which says that the partition algebra is the algebra of all transformations commuting with the action of the symmetric group on tensor products of its permutation representation. In particular, we restrict the action of the symmetric group to the action of the alternating group. In this context, we compute a basis for the centralizer algebra and show when the centralizer is isomorphic to the partition algebra.

Key Words:

• Alternating group
• Centralizer algebra
• Partition algebra

1991 MSC:

• 16S99
• 05E99

Notes

^#Communicated by B. Parshall.