Six identical antenna elements are mounted on a mast with point-group symmetry
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Group theory and symmetry · Group theory and symmetry
Invariance, Ch Representations, Schur's lemma and characters
Problem
Six identical antenna elements are mounted on a mast with point-group symmetry C6v, of order 12, whose elements fall into six classes.
((a)) Using the class count and ∑idi2=∣G∣, find the dimensions of the irreducible representations of C6v.
((b)) Using the degeneracy theorem, state which sizes of degeneracy the array's resonant frequencies can show as a consequence of symmetry alone.
((c)) An engineer measures three resonances at exactly the same frequency. Can this triple coincidence be a symmetry-forced degeneracy of C6v? Explain what it must be instead.