Algebraic Geometry and Combinatorics Seminar: Plane partitions in quantum chemistry

Abstract: The space of quantum states of a system of electrons may be modeled mathematically as an exterior power of a complex vector space. This space carries a natural SU(2)-action, and chemists are often particularly interested in the space of invariants with respect to this group action, called the space of spin adapted quantum states. We describe an explicit basis for this invariant subspace using plane partitions and find its dimension as a complex vector space via an explicit bijection with certain Dyck paths. This is joint work with Ada Stelzer and Svala Sverrisdóttir.

Host: Martha Precup