Non-crystalographic:I_h- Products

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Representation Products:

⊗	Ag	T1g	T2g	Gg	Hg	Au	T1u	T2u	Gu	Hu
Ag	Ag	T1g	T2g	Gg	Hg	Au	T1u	T2u	Gu	Hu
T1g	T1g	Ag+T1g+Hg	Gg+Hg	T2g+Gg+Hg	T1g+T2g+Gg+Hg	T1u	Au+T1u+Hu	Gu+Hu	T2u+Gu+Hu	T1u+T2u+Gu+Hu
T2g	T2g	Gg+Hg	Ag+T2g+Hg	T1g+Gg+Hg	T1g+T2g+Gg+Hg	T2u	Gu+Hu	Au+T2u+Hu	T1u+Gu+Hu	T1u+T2u+Gu+Hu
Gg	Gg	T2g+Gg+Hg	T1g+Gg+Hg	Ag+T1g+T2g+Gg+Hg	T1g+T2g+Gg+2Hg	Gu	T2u+Gu+Hu	T1u+Gu+Hu	Au+T1u+T2u+Gu+Hu	T1u+T2u+Gu+2Hu
Hg	Hg	T1g+T2g+Gg+Hg	T1g+T2g+Gg+Hg	T1g+T2g+Gg+2Hg	Ag+T1g+T2g+2Gg+2Hg	Hu	T1u+T2u+Gu+Hu	T1u+T2u+Gu+Hu	T1u+T2u+Gu+2Hu	Au+T1u+T2u+2Gu+2Hu
Au	Au	T1u	T2u	Gu	Hu	Ag	T1g	T2g	Gg	Hg
T1u	T1u	Au+T1u+Hu	Gu+Hu	T2u+Gu+Hu	T1u+T2u+Gu+Hu	T1g	Ag+T1g+Hg	Gg+Hg	T2g+Gg+Hg	T1g+T2g+Gg+Hg
T2u	T2u	Gu+Hu	Au+T2u+Hu	T1u+Gu+Hu	T1u+T2u+Gu+Hu	T2g	Gg+Hg	Ag+T2g+Hg	T1g+Gg+Hg	T1g+T2g+Gg+Hg
Gu	Gu	T2u+Gu+Hu	T1u+Gu+Hu	Au+T1u+T2u+Gu+Hu	T1u+T2u+Gu+2Hu	Gg	T2g+Gg+Hg	T1g+Gg+Hg	Ag+T1g+T2g+Gg+Hg	T1g+T2g+Gg+2Hg
Hu	Hu	T1u+T2u+Gu+Hu	T1u+T2u+Gu+Hu	T1u+T2u+Gu+2Hu	Au+T1u+T2u+2Gu+2Hu	Hg	T1g+T2g+Gg+Hg	T1g+T2g+Gg+Hg	T1g+T2g+Gg+2Hg	Ag+T1g+T2g+2Gg+2Hg

Transition Products:

For the I_h point group, the irreducible representation of the dipole operator is T_1u. Transitions that are dipole forbidden are indicated by parentheses.

⊗T1u⊗	Ag	T1g	T2g	Gg	Hg	Au	T1u	T2u	Gu	Hu
Ag	(T1u)	(Au+T1u+Hu)	(Gu+Hu)	(T2u+Gu+Hu)	(T1u+T2u+Gu+Hu)	(T1g)	Ag+T1g+Hg	(Gg+Hg)	(T2g+Gg+Hg)	(T1g+T2g+Gg+Hg)
T1g	(Au+T1u+Hu)	(Au+3T1u+T2u+Gu+2Hu)	(T1u+2T2u+2Gu+2Hu)	(T1u+2T2u+3Gu+3Hu)	(Au+2T1u+2T2u+3Gu+4Hu	Ag+T1g+Hg	Ag+3T1g+T2g+Gg+2Hg	(T1g+2T2g+2Gg+2Hg)	(T1g+2T2g+3Gg+3Hg)	Ag+2T1g+2T2g+3Gg+4Hg
T2g	(Gu+Hu)	(T1u+2T2u+2Gu+2Hu)	(2T1u+T2u+2Gu+2Hu)	(Au+2T1u+2T2u+2Gu+3Hu)	(Au+2T1u+2T2u+3Gu+4Hu)	(Gg+Hg)	(T1g+2T2g+2Gg+2Hg)	(2T1g+T2g+2Gg+2Hg)	Ag+2T1g+2T2g+2Gg+3Hg	Ag+2T1g+2T2g+3Gg+4Hg
Gg	(T2u+Gu+Hu)	(T1u+2T2u+3Gu+3Hu)	(Au+2T1u+2T2u+2Gu+3Hu)	(Au+3T1u+2T2u+3Gu+4Hu)	(Au+3T1u+3T2u+4Gu+5Hu)	(T2g+Gg+Hg)	(T1g+2T2g+3Gg+3Hg)	Ag+2T1g+2T2g+2Gg+3Hg	Ag+3T1g+2T2g+3Gg+4Hg	Ag+3T1g+3T2g+4Gg+5Hg
Hg	(T1u+T2u+Gu+Hu)	(Au+2T1u+2T2u+3Gu+4Hu)	(Au+2T1u+2T2u+3Gu+4Hu)	(Au+3T1u+3T2u+4Gu+5Hu)	(Au+4T1u+4T2u+5Gu+6Hu)	(T1g+T2g+Gg+Hg)	Ag+2T1g+2T2g+3Gg+4Hg	Ag+2T1g+2T2g+3Gg+4Hg	Ag+3T1g+3T2g+4Gg+5Hg	Ag+4T1g+4T2g+5Gg+6Hg
Au	(T1g)	Ag+T1g+Hg	(Gg+Hg)	(T2g+Gg+Hg)	(T1g+T2g+Gg+Hg)	(T1u)	(Au+T1u+Hu)	(Gu+Hu)	(T2u+Gu+Hu)	(T1u+T2u+Gu+Hu)
T1u	Ag+T1g+Hg	Ag+3T1g+T2g+Gg+2Hg	(T1g+2T2g+2Gg+2Hg)	(T1g+2T2g+3Gg+3Hg)	Ag+2T1g+2T2g+3Gg+4Hg	(Au+T1u+Hu)	(Au+3T1u+T2u+Gu+2Hu)	(T1u+2T2u+2Gu+2Hu)	(T1u+2T2u+3Gu+3Hu)	(Au+2T1u+2T2u+3Gu+4Hu
T2u	(Gg+Hg)	(T1g+2T2g+2Gg+2Hg)	(2T1g+T2g+2Gg+2Hg)	Ag+2T1g+2T2g+2Gg+3Hg	Ag+2T1g+2T2g+3Gg+4Hg	(Gu+Hu)	(T1u+2T2u+2Gu+2Hu)	(2T1u+T2u+2Gu+2Hu)	(Au+2T1u+2T2u+2Gu+3Hu)	(Au+2T1u+2T2u+3Gu+4Hu)
Gu	(T2g+Gg+Hg)	(T1g+2T2g+3Gg+3Hg)	Ag+2T1g+2T2g+2Gg+3Hg	Ag+3T1g+2T2g+3Gg+4Hg	Ag+3T1g+3T2g+4Gg+5Hg	(T2u+Gu+Hu)	(T1u+2T2u+3Gu+3Hu)	(Au+2T1u+2T2u+2Gu+3Hu)	(Au+3T1u+2T2u+3Gu+4Hu)	(Au+3T1u+3T2u+4Gu+5Hu)
Hu	(T1g+T2g+Gg+Hg)	Ag+2T1g+2T2g+3Gg+4Hg	Ag+2T1g+2T2g+3Gg+4Hg	Ag+3T1g+3T2g+4Gg+5Hg	Ag+4T1g+4T2g+5Gg+6Hg	(T1u+T2u+Gu+Hu)	(Au+2T1u+2T2u+3Gu+4Hu)	(Au+2T1u+2T2u+3Gu+4Hu)	(Au+3T1u+3T2u+4Gu+5Hu)	(Au+4T1u+4T2u+5Gu+6Hu)

• I_h character table