For the following problems $1$ and $2$ below, determine the direct products and reduce them the

old$-$fashioned way. Do not use the multiplication tables in H&B for those two problems. For the

remainder of the problems use the tables in $H$&$B.$ Note these tables are also on Canvas.

What are the irreducible representations of $T_1{T}_2$ in the $O$ point group?

$""B_1{E}_1{E}_2$ in $C_{6v}?$

Determine the following products using the multiplication tables in H&B$.$

a$)E_g{E}_u$ in $D_{4h}$

b$)$ A$"x{E}^{\text{'}}$ in $C_{3h}$

c$)T_{1g}{T}_{2u}$ in $O_h$

d$)E_1^{\text{'}}x{E}_{2}x{E}_3$ in $D_{9h}$

Determine $(T_{2u}{)}^3$ in the $O_h$ point group

Use the multiplication tables in H&B to determine the symmetric and antisymmetric $($the ones

in brackets in the tables$)$ components of $T_1{T}_1$ in the $O$ point group? Do the same in the $Td$

point group.