Dept Math & Stat UiT, Forskningsparken B459
  15 Mar 2024 Wed 13:00-14:00

Henrik Winther (UiT)

"Spin representations and binary numbers"

We consider a construction of the fundamental spin representations of the simple Lie algebras so(n) in terms of binary arithmetic of fixed width integers. This gives the spin matrices as a Lie subalgebra of a Z-graded associative algebra (rather than the usual N-filtered Clifford algebra). Our description gives a quick way to write down the spin matrices, and gives a way to encode some extra structure, such as the real structure that is invariant under the compact real form, for some n. Additionally we can encode the spin representations combinatorially as (coloured) graphs.