On the Decomposition of Cyclic G-Brauer’s Centralizer Algebras
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In this paper, we define the G-Brauer algebras DGf (x), where G is a cyclic group, called cyclic G-Brauer algebras, as the linear span of r-signed 1-factors and the generalized m, k signed partial 1-factors is to analyse the multiplication of basis elementsin the quotient −→I fG(x, 2k). Also, we define certain symmetric matrices−→T [ ]m,k(x) whoseentries are indexed by generalized m, k signed partial 1-factor. We analyse the irreduciblerepresentations of DGf (x) by determining the quotient−→IfG(x, 2k) of DGf (x) by its radical. We also find the eigenvalues and eigenspaces of−→T [ ]m,k(x) for some values of m and k usingthe representation theory of the generalised symmetric group. The matrices T [ ]m,k(x) whoseentries are indexed by generalised m, k signed partial 1-factors, which helps in determiningthe non semisimplicity of these cyclic G-Brauer algebras DGf (x), where G = Zr.
Abstract
In this paper, we define the G-Brauer algebras DGf (x), where G is a cyclic group, called cyclic G-Brauer algebras, as the linear span of r-signed 1-factors and the generalized m, k signed partial 1-factors is to analyse the multiplication of basis elementsin the quotient −→I fG(x, 2k). Also, we define certain symmetric matrices−→T [ ]m,k(x) whoseentries are indexed by generalized m, k signed partial 1-factor. We analyse the irreduciblerepresentations of DGf (x) by determining the quotient−→IfG(x, 2k) of DGf (x) by its radical. We also find the eigenvalues and eigenspaces of−→T [ ]m,k(x) for some values of m and k usingthe representation theory of the generalised symmetric group. The matrices T [ ]m,k(x) whoseentries are indexed by generalised m, k signed partial 1-factors, which helps in determiningthe non semisimplicity of these cyclic G-Brauer algebras DGf (x), where G = Zr.
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