Abstract: Let $G$ be a connected reductive group defined over a nonarchimedean local field of odd residue characteristic. Let $H$ be the fixed points of an involution (automorphism of order two) of $G$. A representation of $G$ is said to be $H$-distinguished if there exists a nonzero $H$-invariant linear functional on the space of the representation.
The $H$-relatively supercuspidal representations of G are the building blocks for the distinguished representations of G. We will describe a method for constructing $H$-relatively supercuspidal representations of $G$. Some examples will be discussed. (Note: Some background info will be presented in the colloquium talk.)
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