Group Orthogonality Theorem
Let Gamma be a representation for a group of group order h, then
| [画像: sum_(R)Gamma_i(R)_(mn)Gamma_j(R)_(m^'n^')^*=h/(sqrt(l_il_j))delta_(ij)delta_(mm^')delta_(nn^'). ] |
The proof is nontrivial and may be found in Eyring et al. (1944).
See also
Group, Group Character, Irreducible RepresentationExplore with Wolfram|Alpha
WolframAlpha
More things to try:
References
Eyring, H.; Walter, J.; and Kimball, G. E. Quantum Chemistry. New York: Wiley, p. 371, 1944.Referenced on Wolfram|Alpha
Group Orthogonality TheoremCite this as:
Weisstein, Eric W. "Group Orthogonality Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GroupOrthogonalityTheorem.html