A NOTE ON THE UNITS OF MANTACI-REUTENAUER ALGEBRA


ARSLAN H. , CAN H.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.55, no.4, pp.1037-1049, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 55 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.4134/bkms.b170496
  • Title of Journal : BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.1037-1049

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 C lambda of G(n), where lambda is an element of BP(n), the equality |C lambda superset of D-A| = |C lambda superset of D-A'| holds. Finally, we have given the general structure of units of Mantaci-Reutenauer algebra.