fˈɜːðɚ, ɪɾ ɪz ɐ nˈɛsᵻsɚɹi kəndˈɪʃən fɚðɪ ɛɡzˈɪstəns əvə nˈɑːnzˈiəɹoʊ hˈɑːməmˌoːɹfɪzəm ʌv sˌʌm hˈaɪɪst wˈeɪt mˈɑːdʒuːlz ɐ hˈɑːməmˌoːɹfɪzəm ʌv sˈʌtʃ mˈɑːdʒuːlz pɹɪzˈɜːvz sˈɛntɹəl kˈæɹɪktɚ.
Further, it is a necessary condition for the existence of a non-zero homomorphism of some highest weight modules (a homomorphism of such modules preserves central character).