In this talk, I will discuss three Cartan subalgebras (or root systems) related to the branching problem of reductive Lie groups. One Cartan subalgebra describes complexity of an embedding of $G$-varieties. This is related to intertwining operators (symmetry breaking operators). The others are defined by the annihilators of $\mathfrak{g}$-modules or their non-zero vectors. They are related to the shape of the (continuous) spectrum. I will also discuss a relation between the Cartan subalgebras and the moment maps for Hamiltonian actions.
De Toshiyuki Kobayashi
De Pierre Julg
De Quentin Labriet
De Víctor Pérez-Valdés
De Guendalina Palmirotta
De Christian Arends
De Tomasz Przebinda
De Masatoshi Kitagawa
De Janet Flikkema
De Robin van Haastrecht
De Tatsuro Hikawa
De Temma Aoyama
De Yuichiro Tanaka
De Pierre Clare
De Neza Zager Korenjak
De Colin Davalo
