December 5, Wednesday, 18:30, room 306

Yury Rudko

Gelfand-Zetlin bases for representations of SL(n)

We construct Gelfand-Zetlin bases in irreducible representations of SL(n) using the chain of subgroups SL(n)>SL(n-1)>…>SL(2). The key step is reduction of an irreducible representation of SL(n) to SL(n-1). Using reduction we show that basis vectors are labeled by lattice points in a convex polytope (called Gelfand-Zetlin polytope) defined by simpe inequalities. We work out concrete examples such as the adjoint representation of SL(3).