In this paper, we obtain the trace functions of Mantaci-Reutenauer algebra $\mathcal{MR}(W_{n})$, where $(W_{n},S_{n})$ is a Coxeter system of type $B_{n}$. We also show for every $\lambda \in \mathcal{DP}(n)$ that each characteristic class function $e_{\lambda}$ of the group $W_{n}$ is a trace function of Mantaci-Reutenauer algebra, where $\mathcal{DP}(n)$ stands for the set of all double partitions of $n$. Since the dimension of the trace function space on the Mantaci-Reutenauer algebra is $|\mathcal{DP}(n)|$, it exactly coincides with the algebra $\mathbb{Q}\textrm{Irr}W_{n}$ generated by the irreducible characters of the group $W_{n}$. Although the multiplication of basis elements $d_{A}$ and $d_{A'}$ is not commutative in Mantaci-Reutenauer algebra, the images of $d_{A}d_{A'}$ and $d_{A'}d_{A}$ under $e_{\lambda}$ are equal to each other.
Mantaci-Reutenauer algebra Orthogonal primitive idempotent Trace function
Birincil Dil | İngilizce |
---|---|
Konular | Mühendislik |
Bölüm | Articles |
Yazarlar | |
Yayımlanma Tarihi | 15 Nisan 2018 |
Gönderilme Tarihi | 31 Mayıs 2017 |
Kabul Tarihi | 20 Mart 2018 |
Yayımlandığı Sayı | Yıl 2018 Cilt: 6 Sayı: 1 |