Question

For T_d verify for each of the irreducible representations rule #5.

Rule 5) For any give irreducible representation the sum of the squares of the characters multiplied by the number of operations in the class equals the order of the group

Answer 1

the sum of squares of characters of the identity operations in the iresps is equal to h, which is the order of the group

.................(1)

For Td geometry if we see the table the order, h = 24

To prve the above rule Lets consider the identity operation, E ........ keep the character table in front you can see for E ....A1 = 1, A2 = 1, E=2, T1 = 3 , T2 = 3 now put these values in the formula (1)

which gives us

which proves this rule .................similarly you can get values for other operations