Algebra Seminar: Ryom-Hansen -- Graded cellular basis and Jucys-Murphy elements for the generalized blob algebra

Steen Ryom-Hansen (Universidad de Talca) 

Wednesday 6 March, 12-1pm, Place: Carslaw 375 

Title: Graded cellular basis and Jucys-Murphy elements for the generalized blob algebra 

Abstract: The generalized blob algebra b_n was introduced by Martin and Woodcock.  It
can be considered as a higher level Temperley-Lieb algebra, although there is no natural
diagram calculus associated with b_n.  The representation theory of the Temperley-Lieb
algebra can be seen as a toy model for modular representation theory, but this is not at
all the case for the representation theory for b_n, which appears to contain ’the full
story’.  In the talk we shall explain how to construct a graded cellular basis for b_n
in any characteristic.  A first step is here given by the Brundan-Kleshchev and Rouquier
isomorphism between the cyclotomic KLR-algebra and the cyclotomic Hecke algebra.  A main
obstacle is here that the known cellular structure on the cyclotomic Hecke algebra is
related to the dominance order on multipartitions, which is badly behaved on b_n.