Reciprocity in character theory of finite semigroups

✍ Scribed by Mohan S. Putcha

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 117 KB
• Volume: 163
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(00)00162-6

✦ Synopsis

This paper concerns the complex characters of ÿnite semigroups. We begin by reducing the general problem to the study of local monoids M = G ∪ J ∪ {0}, where G is the unit group and J is a regular J-class. Let H be a maximal subgroup of J . For a CH -module U with character Â, let Ũ be the associated CM -module and let Ẫ be the character of the CG-module Ũ . For a CG-module V with character , we construct a natural CH -module V ∼ with character ∼ . We prove the reciprocity theorem: Ẫ; G = Â; ∼ H . As a consequence we ÿnd a characterization of the J -cuspidal characters of G. We go on to interpret our results for groups, introducing the concept of double parabolic induction.