 Solution

ID: past-exam-of-the-introduction-to-representation-theory-course-of-the-university-of-oxford/2023/2/a/solution

χ_{Ind_{H}^{G} W} (g) = \frac{1}{∣ H ∣} x \in G x^{- 1} gx \in H \sum χ_{W} (x^{- 1} gx) .

Equivalently, extend the character

χ_{W}

by zero outside the subgroup

H

and sum over all

x \in G

. The factor

1/∣ H ∣

accounts for passing from elements of

G

to representatives of left cosets of

H

 New to topics? Read the docs here!