An application of TQFT to modular representation theory

For \(p\ge 5\) a prime, and \(g\ge 3\) an integer, we use Topological Quantum Field Theory (TQFT) to study a family of \(p-1\) highest weight modules \(L_p(\lambda )\) for the symplectic group \({{\mathrm{Sp}}}(2g,K)\) where K is an algebraically closed field of characteristic p. This permits explicit formulae for the dimension and the formal character of \(L_p(\lambda )\) for these highest weights.