Character Table

A character table lists the Irreducible Representations of a Group, and other information.

We will consider the character table for C_{2v}. Those rows of integers, mostly -1 and +1, are Irreducible Representations.

We consider the operations on the y-axis.

E(y)=+1 y

C_2(y)= -1 y

\sigma_{xz}(y)= -1 y

\sigma_{yz}(y)= +1 y

At this point we have used all three axes to get irreducible representations. We need one more because the number of irreducible representations equals the number of symmetry elements.

Next we consider the operations on the x axis.

E(x)=+1 x

C_2(x)= -1 y

\sigma_{xz}(y)= -1 y

\sigma_{yz}(y)= +1 y

Next we consider the operations on the z axis.

E(z)=+1 z

C_2(z)= +1 z

\sigma_{xz}(x)= +1 z

\sigma_{yz}(z)= +1 z

C_2(x)= -1 y

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Mulliken Symbols

The symbols on the right side are Mulliken symbols.