A Note About the Trace Functions on Mantaci--Reutenauer Algebra

Hasan Arslan [1]

19 21

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
  • [1] Arslan, H., Descent Algebras of Bn-type Coxeter Groups, PhD Thesis, Erciyes University, 2015.
  • [2] C. Bonnaf´e and C. Hohlweg, Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups, Ann. Inst. Fourier (Grenoble) Volume:56 No.1 (2006), 131-181.
  • [3] C. Bonnaf´e, Representation theory of Mantaci-Reutenauer algebras, Algebr. Represent. Theory Volume: 11, No.4 (2008), 307-346.
  • [4] M. Geck, Trace functions on Iwahori-Hecke algebras, Knot theory (Warsaw, 1995), Banach Center Publ., Polish Acad. Sci., Warsaw Volume:42 (1998), 87–109.
  • [5] Geck, M. and Pfeiffer, G., Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras, London Mathematical Society Monographs, New Series, vol. 21, The Clarendon Press, Oxford University Press, New York, 2000.
  • [6] R. Mantaci and C. Reutenauer A generalization of Solomon’s algebra for hyperoctahedral groups and other wreath products, Comm. Algebra Volume:23, No.1 (1995), 27-56.
  • [7] L. Solomon, A Mackey formula in the group ring of a Coxeter group, Journal of Algebra Volume:41, No.2 (1976), 255-264.
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Yazar: Hasan Arslan
E-posta: hasanarslan@erciyes.edu.tr
Kurum: Erciyes University, Faculty of Science, Mathematics Department, 38039, Melikgazi, Kayseri
Ülke: Turkey


Bibtex @araştırma makalesi { konuralpjournalmath317697, journal = {Konuralp Journal of Mathematics}, issn = {}, address = {Mehmet Zeki SARIKAYA}, year = {}, volume = {6}, pages = {140 - 143}, doi = {}, title = {A Note About the Trace Functions on Mantaci--Reutenauer Algebra}, key = {cite}, author = {Arslan, Hasan} }
APA Arslan, H . (). A Note About the Trace Functions on Mantaci--Reutenauer Algebra. Konuralp Journal of Mathematics, 6 (1), 140-143. Retrieved from http://dergipark.gov.tr/konuralpjournalmath/issue/31478/317697
MLA Arslan, H . "A Note About the Trace Functions on Mantaci--Reutenauer Algebra". Konuralp Journal of Mathematics 6 (): 140-143 <http://dergipark.gov.tr/konuralpjournalmath/issue/31478/317697>
Chicago Arslan, H . "A Note About the Trace Functions on Mantaci--Reutenauer Algebra". Konuralp Journal of Mathematics 6 (): 140-143
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