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On the centralizer algebra of the unitary reflection group G(m,p,n)

Published online by Cambridge University Press:  22 January 2016

Kenichiro Tanabe
Kenichiro Tanabe*
Affiliation:
Graduate School of Mathematics, Kyushu University, Fukuoka 812-81, Japan, tanabe@math.kyushu-u.ac.jp
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Abstract

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The imprimitive unitary reflection group G(m, p, n) acts on the vector space V =Cn naturally. The symmetric group Sk acts on ⊗kV by permuting the tensor product factors. We show that the algebra of all matrices on ⊗kV commuting with G(m, p, n) is generated by Sk and three other elements. This is a generalization of Jones’s results for the symmetric group case [J].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 148 , December 1997 , pp. 113 - 126
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1997

References

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