Worksheet: Reducible and Irreducible Representations

In this worksheet, we will practice defining reducible and irreducible representations and relating their characters to the order of the group.

Q1:

The character table for the Dh group is given below. How many 3D irreducible representations are there in this group?

DhE2C3C𝜎h2S3𝜎v
A111111𝑥+𝑦,𝑧
A111111𝑅
E210210𝑥,𝑦𝑥𝑦,𝑥𝑦
A111111
A111111𝑧
E210210𝑅,𝑅𝑥𝑧,𝑦𝑧

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