 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-3/19i/a/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

For an

H

-module

W

Ind_{H}^{G} W = C [G] \otimes_{C [H]} W .

The action is left multiplication on the first factor:

g_{0} \cdot (g \otimes w) = g_{0} g \otimes w .

It is well defined because the tensor relation

g h \otimes w = g \otimes h w

is preserved by left multiplication.

 New to topics? Read the docs here!