Integrality conjecture for functional dimensions

Let $G$ be a connected unipotent algebraic group, let $e$ be a minimal idempotent of ${\mathscr D}_G(G)$ , and let its functional dimension be $d_e=(\dim G-n_e)/2$ . The integrality conjecture. If the ${\mathbb L}$ -packet corresponding to $e$ is trivial, then $d_e$ is an integer.

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Primary source

Mitya Boyarchenko and Vladimir Drinfeld, “A motivated introduction to character sheaves and the orbit method for unipotent groups in positive characteristic”, arXiv:math/0609769 (2010).

character-sheaves representation-theory unipotent-groups

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