What is the way to deal with a husband's jealousy of his wife's intense admiration for deceased religious figures like Omar ibn al-Khattab, and how can she be persuaded to stop repeatedly mentioning her admiration to avoid provoking this jealousy?

Jealousy is of two types: praiseworthy in situations of suspicion, and blameworthy in situations other than those of suspicion. The Prophet, peace and blessings be upon him, clarified this by saying: "Indeed, there is jealousy that Allah loves and jealousy that Allah detests. As for the jealousy that Allah loves, it is jealousy in suspicion. As for the jealousy that Allah detests, it is jealousy without suspicion." Your jealousy regarding your wife's discussion of Umar ibn al-Khattab, may Allah be pleased with him, is blameworthy jealousy, because there is no suspicion in it. The love of Umar, may Allah be pleased with him, is a sign of faith.