In the seminar we discuss construction of exceptional algebraic groups, both split and non-split via Jordan algebras and composition algebras. We further plan to discuss minimal representations on those groups and the theta correspondence for dual pairs in exceptional groups. Occasionally, guest lectures on various topics on representation theory and automorphic forms will take place.

The seminar meets on Wednesdays, 10:10-12:00, in 58-201

2019–20–A meetings

Thu, Jan 23, 16:10–17:00 The algebraic symmetry of the hydrogen atom Eyal Subag (Penn State)

The hydrogen atom system is a fundamental example of a quantum mechanical system. Symmetry plays the main role in our current understanding of the system. In this talk I will describe a new type of algebraic symmetry for the system. I will show that the collection of all regular solutions of the Schrödinger equation is an algebraic family of representations of different algebras. Such a family is known as an algebraic family of Harish-Chandra modules. The algebraic family has a canonical filtration from which the physically relevant solutions and the spectrum of the Schrödinger operator can be recovered.

If time permits I will relate the spectral theory of the Schrödinger operator to the algebraic family. No prior knowledge about quantum mechanics or representation theory will be assumed.

Seminar run by Prof. Nadya Gurevich