A note on the units of Mantaci-Reutenauer algebra
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In this paper, we have first presented the construction of the linear characters of a finite Coxeter group $G_{n}$ of type $B_{n}$ by lifting all linear characters of the quotient group $G_{n}/[G_{n},G_{n}]$ of the commutator subgroup $[G_{n},G_{n}]$. Also we show that the sets of distinguished coset representatives $D_{A}$ and $D_{A'}$ for any two signed compositions $A, A'$ of $n$ which are $G_{n}$-conjugate to each other and for each conjugate class $\mathcal{C}_{\lambda}$ of $G_{n}$, where $\lambda \in \mathcal{BP}(n)$, the equality $|\mathcal{C}_{\lambda} \cap D_{A}|=|\mathcal{C}_{\lambda} \cap D_{A'}|$ holds. Finally, we have given the general structure of units of Mantaci-Reutenauer algebra.
Abstract
In this paper, we have first presented the construction of the linear characters of a finite Coxeter group $G_{n}$ of type $B_{n}$ by lifting all linear characters of the quotient group $G_{n}/[G_{n},G_{n}]$ of the commutator subgroup $[G_{n},G_{n}]$. Also we show that the sets of distinguished coset representatives $D_{A}$ and $D_{A'}$ for any two signed compositions $A, A'$ of $n$ which are $G_{n}$-conjugate to each other and for each conjugate class $\mathcal{C}_{\lambda}$ of $G_{n}$, where $\lambda \in \mathcal{BP}(n)$, the equality $|\mathcal{C}_{\lambda} \cap D_{A}|=|\mathcal{C}_{\lambda} \cap D_{A'}|$ holds. Finally, we have given the general structure of units of Mantaci-Reutenauer algebra.
참고문헌 (8)
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