Work

Homomorphisms from Specht Modules to Signed Young Permutation Modules

Year: 2018

Type: article

Abstract: We construct a class Θ R of homomorphisms from a Specht module S λ Z to a signed permutation module M Z (α|β) which generalises James's construction of homomorphisms whose codomain is a Young permutation module.We show that any φ ∈ Hom ZSn S λ Z , M Z (α|β) lies in the Q-span of Θ sstd , a subset of Θ R corresponding to semistandard λ-tableaux of type (α|β).We also study the conditions for which Θ F sstd -a subset of Hom FSn S λ F , M F (α|β) induced by Θ sstd -is linearly independent, and show that it is a basis for Hom FSn S λ F , M F (α|β) when FS n is semisimple.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2018.038

Authors: Kay Jin Lim, Kai Meng Tan

Institutions: Nanyang Technological University, National University of Singapore

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Ministry of Education, India

OpenAlex ID: W2734617398