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Speaker:
Rosa Orellana, Dartmouth
Title:
Partition Algebras of type B
Abstract:
The partition algebras were first introduced by V. Jones and P.
Martin as a generalization of the Temperley-Lieb algebras. The
construction of the algebra given by Martin was via a basis given
by set partions of a 2n-element set. On the other hand, Jones
constructed a centralizer algebra of the symmetric group and
showed that it had a basis indexed by set partitions.
In this talk I will use set partitions of type B and construct
a type B partition algebra. I will also show that there is a
Schur-Weyl duality of this algebra with the group algebra of the
hyperoctahedral group.
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