Products of class-sums of the alternating group

Tekin S., Katriel J.

PUBLICATIONES MATHEMATICAE-DEBRECEN, vol.62, pp.43-52, 2003 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 62
  • Publication Date: 2003
  • Journal Name: PUBLICATIONES MATHEMATICAE-DEBRECEN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.43-52
  • Istanbul Technical University Affiliated: No

Abstract

Most of the structure constants in the class-algebra of the alternating group, A(n) can be expressed in terms of corresponding structure constants in the class-algebra of the symmetric group, S-n.This statement has to be modified for A(n)-structure constants that involve more than one conjugacy class stemming from a common S-n conjugacy class, when the latter consists of cycles of odd and distinct lengths. The A(n)-structure constants of the latter type depend on the S-n character that corresponds to the self-conjugate Young diagram whose principal hook lengths are equal to the set of odd and distinct cycle lengths mentioned above, evaluated over the third conjugacy class involved. The results provide a combinatorial interpretation of the S-n self-conjugate irreducible characters.