The Garnir relations for Weyl groups of type C-n

Can H.

ELECTRONIC JOURNAL OF COMBINATORICS, vol.15, no.1, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 1
  • Publication Date: 2008
  • Journal Name: ELECTRONIC JOURNAL OF COMBINATORICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Erciyes University Affiliated: Yes

Abstract

The Garnir relations play a very important role in giving combinatorial constructions of representations of the symmetric groups. For the Weyl groups of type C-n, having obtained the alternacy relation, we give an explicit combinatorial description of the Garnir relation associated with a Delta-tableau in terms of root systems. We then use these relations to find a K-basis for the Specht modules of the Weyl groups of type C-n.