Group Representations on the Homology of Products of Posets

✍ Scribed by Sheila Sundaram; Volkmar Welker

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 332 KB
• Volume: 73
• Category: Article
• ISSN: 0097-3165
• DOI: 10.1006/jcta.1996.0013

✦ Synopsis

In this note we give a description of the representation of the wreath product S n [G] of the symmetric group S n and a finite group G on the homology of the product of n copies of a partially ordered set (poset for short) P on which G acts as a group of automorphisms. In the sequel all posets will be finite. We will consider three types of product constructions. The direct product P_Q of two posets P and Q is the poset on the Cartesian product P_Q whose order relation is defined by (x, y)