OIST Representation Theory Seminar

Dean Yates, Queen Mary University of London

Title: Spin representations of the symmetric group

Abstract: Spin representations of the symmetric group S_n can be thought of equivalently as either projective representations of S_n, or as linear representations of a double cover S_n⁺ of S_n. Whilst the linear representation theory of S_n is dictated by removing ‘rim-hooks’ from (the Young diagrams of) partitions of n, the projective representation theory of S_n is controlled by removing ‘bars’ from bar partitions of n (i.e. partitions of n into distinct parts). We will look at some combinatorial results on bar partitions from a recent paper of the author before discussing methods for determining the modular decomposition of spin representations over fields of positive characteristic.