Spin representations of the symmetric group Sn can be thought of equivalently as either projective representations of Sn, or as linear representations of a double cover Sn+ of Sn. Whilst the linear representation theory of Sn is dictated by removing ‘rim-hooks’ from (the Young diagrams of) partitions of n, the projective representation theory of Sn 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.
This video was produced by the Okinawa Institute of Science and Technology, as part of their OIST Representation Theory Seminar series.
