Type: Seminar

Distribution: World

Expiry: 12 Apr 2019

CalTitle1: Algebra Seminar: Graded cellular basis and Jucys-Murphy elements for the generalized blob algebra

Auth: kevinc@10.17.64.168 (kcou7211) in SMS-WASM

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.