Tabloids and weighted sums of characters of certain modules of the symmetric groups

We consider certain modules of the symmetric groups whose basis elements are called tabloids. As modules of the symmetric groups, some of these are isomorphic to Springer modules. We give a combinatorial description for weighted sums of their characters; we introduce combinatorial objects called (, l)tableaux, and rewrite weighted sums of characters as the numbers of these combinatorial objects. We also consider the meaning of these combinatorial objects; we construct a correspondence between (, l)-tableaux and tabloids whose images are eigenvectors of the action of an element of cycle type in quotient modules. R

• Type: Journal
• Year: 2008
• Where: EJC
• Authors: Yasuhide Numata
• Keywords: Combinatorial Objects, EJC 2007, EJC 2008, Information Technology, Nous, Symmetric Groups