SMS scnews item created by Anthony Henderson at Fri 29 Feb 2008 1656
Type: Seminar
Distribution: World
Expiry: 7 Mar 2008
Calendar1: 7 Mar 2008 1205-1255
CalLoc1: Carslaw 373
CalTitle1: Algebra Seminar: Mathas -- Cyclotomic Solomon algebras
Auth: anthonyh@asti.maths.usyd.edu.au

Algebra Seminar

Cyclotomic Solomon algebras

Andrew Mathas

7th March, 12:05-12:55pm, Carslaw 373


Abstract

This talk is about an analogue of the Solomon descent algebra for the complex reflection groups of type G(r,1,n). As with the Solomon descent algebra, our algebra has a basis given by sums of "distinguished" coset representatives for certain "reflection subgroups". We explicitly describe the structure constants with respect to this basis and show that they are polynomials in r. This allows us to define a deformation, or q-analogue, of these algebras which depends on a parameter q. We determine the irreducible representations of all of these algebras and give a basis for their radicals. Finally, we show that the direct sum of cyclotomic Solomon algebras is canonically isomorphic to a concatenation Hopf algebra.

This is joint work with Rosa Orellana (Dartmouth).


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