University of Sydney Algebra Seminar
James East
(University of Sydney)
Friday 11th November, 12.0512.55pm, Carslaw 157
Cellular algebras and inverse semigroups
Cellular algebras were introduced by Graham and Lehrer in 1996 to provide a
unified framework for understanding the representation theory of several
important algebras; examples include Hecke algebras of types A and B, Brauer
algebras, TemperleyLieb algebras, partition algebras and many more. In this
talk we will investigate the cellularity of another class of algebras  the
inverse semigroup algebras. The semigroup algebra of a finite inverse
semigroup turns out to be cellular if (i) the group algebras of its maximal
subgroups are cellular, and (ii) the antiinvolutions on these maximal
subgroup algebras are compatible in a certain sense. We will investigate
several key examples including the symmetric inverse semigroup (also known
as the rook monoid) and the dual symmetric inverse semigroup. If time
permits we will conclude with a review of some recent work of Wilcox who has
extended these ideas to study a wider class of semigroups.
