The varieties for some Specht modules

• Main Author: Lim, Kay Jin
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2014
• Subjects: DRNTU::Science::Mathematics::Algebra
• Online Access: https://hdl.handle.net/10356/102335; http://hdl.handle.net/10220/18897
• Institution: Nanyang Technological University

J. Carlson introduced the cohomological and rank variety for a module over a finite group algebra. We give a general form for the largest component of the variety for the Specht module for the partition (pp) of p2 restricted to a maximal elementary abelian p-subgroup of rank p. We determine the varieties of a large class of Specht modules corresponding to p-regular partitions. To any partition of np of not more than p parts with empty p-core we associate a unique partition Φ(μ) of np, where the rank variety of the restricted Specht module SμEn↓ to a maximal elementary abelian p-subgroup En of rank n is V#En (k) if and only if V#En (SΦ(μ)) = V#En (k). In some cases where Φ(μ) is a 2-part partition, we show that the rank variety V#En (Sμ) is V#En (k). In particular, the complexity of the Specht module Sμ is n.