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A NOTE ON THE UNITS OF MANTACI-REUTENAUER ALGEBRA

  • Arslan, Hasan (Department of Mathematics Erciyes University) ;
  • Can, Himmet (Department of Mathematics Erciyes University)
  • 투고 : 2017.06.02
  • 심사 : 2018.05.29
  • 발행 : 2018.07.31

초록

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 $D_{A^{\prime}}$ 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 ${\mid}{\mathcal{C}}_{\lambda}{\cap}D_A{\mid}={\mid}{\mathcal{C}}_{\lambda}{\cap}D_{A^{\prime}}{\mid}$ holds. Finally, we have given the general structure of units of Mantaci-Reutenauer algebra.

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참고문헌

  1. H. Arslan and H. Can, Generalized Burnside algebra of type $B_n$, http://arxiv.org/abs/1410.8390.
  2. C. Bonnafe, Representation theory of Mantaci-Reutenauer algebras, Algebr. Represent. Theory 11 (2008), no. 4, 307-346. https://doi.org/10.1007/s10468-007-9074-1
  3. C. Bonnafe and C. Hohlweg, Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups, Ann. Inst. Fourier (Grenoble) 56 (2006), no. 1, 131-181. https://doi.org/10.5802/aif.2176
  4. C. Bonnafe and G. Pfeiffer, Around Solomon's descent algebras, Algebr. Represent. Theory 11 (2008), no. 6, 577-602. https://doi.org/10.1007/s10468-008-9090-9
  5. P. Fleischmann, On pointwise conjugacy of distinguished coset representatives in Coxeter groups, J. Group Theory 5 (2002), no. 3, 269-283. https://doi.org/10.1515/jgth.2002.002
  6. M. Geck and G. Pfeiffer, Characters of finite Coxeter groups and Iwahori-Hecke algebras, London Mathematical Society Monographs. New Series, 21, The Clarendon Press, Oxford University Press, New York, 2000.
  7. R. Mantaci and C. Reutenauer, A generalization of Solomon's algebra for hyperoctahedral groups and other wreath products, Comm. Algebra 23 (1995), no. 1, 27-56. https://doi.org/10.1080/00927879508825205
  8. L. Solomon, A Mackey formula in the group ring of a Coxeter group, J. Algebra 41 (1976), no. 2, 255-264. https://doi.org/10.1016/0021-8693(76)90182-4