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(2005 / vol.8 / no.2)
A diagram realization of complex reflection groups and Schur-Weyl dualities
Dongho Moon
Pages. 119-127     



We describe elements of the complex reflection group $G(r,1,n)$
using $r$-decorated $n$-diagrams. We also construct a representation
of $G(r,1,n)$ on a tensor product space which commutes with the
action of Lie group $G=GL(m_0) imes cdots imes GL(m_{r-1})$. We
also give a Schur-Weyl duality for the complex reflection group
$G(r,1,n)$ and $G$ on the tensor product space.



1. Coxeter groups and Complex reflection groups
2. Symmetric groups and diagrams
3. Complex reflection group $ G(r,1, n)$ and diagrams
4. Schur-Weyl Duality of $G(r,1,n)$



Coxeter Groups, Complex Reflection Groups, Schur-Weyl Dualities



20C05, 05F15