Dipendra Prasad
IIT Bombay
February 22, 2024
Character theory at special elements: There seems to be a relationship between irreducible characters of finite groups or of compact Lie group $G$ at special elements in $G$ and the dimension of irreducible representations of the centraliser of that element in $G$. For example this happens for the symmetric group on elements whose cycle decomposition has cycles of the same length, and also for compact unitary groups. We discuss some of the results due to me and others, and some framework to think about them for general reductive groups.
IIT Bombay
February 22, 2024
Character theory at special elements: There seems to be a relationship between irreducible characters of finite groups or of compact Lie group $G$ at special elements in $G$ and the dimension of irreducible representations of the centraliser of that element in $G$. For example this happens for the symmetric group on elements whose cycle decomposition has cycles of the same length, and also for compact unitary groups. We discuss some of the results due to me and others, and some framework to think about them for general reductive groups.