Event № 320
The subject of harmonic analysis on Lie groups is well studied but can be rather opaque for non-experts. For the Heiseberg Lie group, or more specifically its Lie algebra, there exists the so-called Weyl transform: a linear map that allows one to define functions on the Lie algebra in a straightforward manner. However abstract the original Lie algebraic definitions might be, it will be shown that all objects of interest can be brought into the form of explicit orthogonal function expansions on concrete spaces. The focus of this talk will be to describe a short path from foundational principles to a kind of noncommutative polar coordinates on the Heisenberg Lie algebra, during which many interesting connections to spectral and representation theory will be manifest.