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Oct 15, 2019 at 0:21 comment added Jim Humphreys The comolex seting adds nothing here. For sources, see the 1967-68 Steinberg lectures at Yale Lectures on Chevalley groups (in the somewhat edited and tpeset version now puboished by the AMS), or seeJantezn's book Representations of Algebraic Groups (now also published by the AMS), for a more comprehensive treatment.
Oct 10, 2019 at 5:36 comment added user130903 Sure. A connected reductive group is generated by a central torus and a semisimple group. On any irreducible representation space, the torus must act by a character, so the restriction to the semisimple group stays irreducible.
Oct 9, 2019 at 14:06 history asked D_S CC BY-SA 4.0