University of Sydney Algebra Seminar

Alex Molev (University of Sydney)

Friday 26th November, 12.05-12.55pm, Carslaw 175

Combinatorial bases for representations of the Lie superalgebra gl(m|n)

Covariant tensor representations of gl(m|n) occur as irreducible components of tensor powers of the natural (m+n)-dimensional representation. We construct a basis of each covariant representation which has the property that the natural Lie subalgebras gl(m) and gl(n) act in this basis by the classical Gelfand-Tsetlin formulas. The main role in the construction is played by the fact that the subspace of gl(m)-highest vectors in any finite-dimensional irreducible representation of gl(m|n) carries a structure of an irreducible module over the Yangian Y(gl(n)). One consequence is a new proof of the character formula for the covariant representations first found by Berele and Regev and by Sergeev.