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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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