Multiplicative Bases for the Centres of the Group Algebra and Iwahori-Hecke Algebra of the Symmetric Group · arXivDesk1205.6837May 30, 20126 pages. To appear in Proceedings of the Southeastern Lie Theory Workshop Series, Proceedings of Symposia in Pure Mathematics
Multiplicative Bases for the Centres of the Group Algebra and Iwahori-Hecke Algebra of the Symmetric Group
Andrew Francis, Lenny Jones
Abstract
Let _n be the Iwahori-Hecke algebra of the symmetric group Sn, and let Z(_n) denote its centre. Let B=b1,b2,...,bt
be a basis for
Z(_n)
over
R=Z[q,q−1] . Then
is called multiplicative if, for every
and
, there exists
such that
bibj=bk . In this article we prove that there are no multiplicative bases for
and
Z(_n)
when
. In addition, we prove that there exist exactly two multiplicative bases for
and none for
Z(₂)
.