The University of Michigan Combinatorics Seminar
Winter 2000
March 10, 4:10-5:00, 3866 East Hall

Superdeterminants and representations
of Lie superalgebras

Tadeusz Józefiak

Mathematical Reviews


A description of irreducible tensor representations of general linear Lie superalgebras (over a field of characteristic zero) in tensor powers of the standard representation has been known since mid 1980s from works of A.N.Sergeev, and A.Berele and A.Regev. In the talk, I will present more explicit construction in terms of products of superdeterminants in the tensor product of polynomial and exterior algebras. A basis description of each irreducible tensor module will also be given. This approach allows us to provide a functorial presentation of irreducible representations as factors of the tensor product of exterior powers [symmetric powers] of the standard module modulo certain relations which will be explicitly described. They correspond to quadratic relations among superdeterminants and are counterparts of relations which have appeared in works of J.Towber and W.Fulton for general linear groups.