G-colored partition algebras as centralizer algebras of wreath products

✍ Scribed by Matthew Bloss

• Book ID: 104140635
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 236 KB
• Volume: 265
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00132-7

✦ Synopsis

Let G be a group. We define an associative algebra P k (x; G) that is a partition algebra whose diagrams have oriented edges labeled by elements of G. For G finite, we show that P k (x; G) is the centralizer algebra of an action of the wreath product G S n on tensor powers of its permutation module.