Let $G$ be an algebraic group defined over a finite field $\mathbb{F}_q$ and let $m$ be a positive integer. Shintani descent is a relationship between the character theories of the two finite groups $G(\mathbb{F}_q)$ and $G(\mathbb{F}_{q^m})$ of $\mathbb{F}_q$ and $\mathbb{F}_{q^m}$-valued points of $G$ respectively. This was first studied by Shintani for $G=GL_n$. Later, Shoji studied Shintani descent for connected reductive groups and related it to Lusztigâ€™s theory of character sheaves. In this talk, I will speak on the cases where $G$ is a unipotent or solvable algebraic group. I will also explain the relationship with the theory of character sheaves.

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Last updated: 18 May 2024