This thesis is in two parts. Part A is concerned with a\ud problem in the representation theory of semisimple algebraic\ud groups. In part B we are interested in the endomorphism rings of\ud comodules, in particular in the endomorphism ring of a certain\ud induced comodule. The parts are more or less self contained\ud each having its own introduction and references. There is\ud however an underlying theme of induction and so the exposition\ud of 2, (A) is relevent to both parts. Other points of overlap\ud are the second theorem of 4 in part A and the digression of\ud 2 in part B
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