Algebra Seminar: Enyang -- A seminormal form for partition algebras

There will be an Algebra Seminar on Friday 2 December, given by John Enyang.  Note the
unusual room.  

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Speaker: John Enyang (University of Sydney) 

Date: Friday 2 December 

Time: 12:05-12:55pm 

Venue: Carslaw 375 

Title: 

A seminormal form for partition algebras 

Abstract: 

Partition algebras were defined by Jones and Martin in the 1990s in connection with the
Potts model and higher dimensional statistical mechanics.  Jones showed that the
partition algebras are in Schur-Weyl duality with the group algebra of the symmetric
group $S_n$ acting on the k-fold tensor power of its n–dimensional permutation
representation $V$ .  In this talk we will introduce a new presentation of the partition
algebras and show how this presentation can be used to obtain explicit combinatorial
formulae for the seminormal representations of the partition algebras.  Our results
generalise to the partition algebras the classical formulae given by Young for the
symmetric group.  

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Anne Thomas - [email protected] 
Seminar website - http://www.maths.usyd.edu.au/u/AlgebraSeminar/