## Different Formula For the Character of an Induced Representation (Pt. III)

**Point of Post: **This post is a continuation of this one.

Thus,

That said, note that for one has

Thus, is equal the diagonal entry of the matrix corresponding to for with respect to the basis . Thus,

And thus, finally putting it all together

**References:**

1. Simon, Barry. *Representations of Finite and Compact Groups*. Providence, RI: American Math. Soc., 1996. Print.

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