"Any controversy which is for the sake of Heaven will endure; and that which is not for the sake of Heaven will not endure. What is a controversy that is for the sake of Heaven? The controversy between Hillel and Shammai. And which is not for the sake of Heaven? The controversy of Korach and all his faction. (Avot 5:17)

"…The Name of Heaven" [in Hebrew, "Leshem Shamayim"] refers to two sefirot: "Shem" denotes malchut, and "shamayim" signifies tiferet. Hence "Leshem Shamayim" denotes the unity of tiferet and malchut as it is known in Kabbalistic terminology. Hillel, however, maintained that from the outset the light can be elicited from above…

"…Hillel and Shammai" disagreed "Leshem Shamayim" - both of them brought about the unity of tiferet and malchut. However, Hillel (whose soul-root was in the sefira of chesed) was of the view that his unity is brought about from above, whereas Shammai (whose soul-root was in the sefira of gevura) maintained that the unity is brought about from below. This means that Shammai argued that a person must first purify and elevate himself, so that he can be a fitting vessel for G‑dly light. This is the proper way to achieve the unity. Hillel, however, maintained that from the outset the light can be elicited from above, and this will purify the person and make him a proper vessel to contain it.

"…Will endure": In fact, both types of service - raising and purifying the vessels, and drawing down the light from above - are necessary. This is comparable to Torah (which descended below from above) and prayer (by which a man raises and purifies himself). Now, prior to the final ruling as to which view to follow, either view was correct, and a person could follow whichever he chose, based on the root of his soul. Korach and his band intended to demolish supernal unity…

However, once Jewish Law was determined in favor of the School of Hillel, it is G‑d's will that the unity will come about only in this way - and, thus, everyone must follow the method of the School of Hillel. Nevertheless, in the World to Come, the law will be decided in favor of the School of Shammai, and everyone will follow his view.

"…A controversy that is not for the sake of Heaven": the Mishna does not write that Korach and Aaron quarreled, only that Korach and his faction quarreled. Korach and his band intended to demolish supernal unity. He wanted to separate between "Shem" (malchut) and "Shamayim" (tiferet). The result of this quarrel was that Korach and his faction did not endure. Rather, Moses and Aaron endured, for their intention was for the sake of Heaven, in order to bring about supernal unity.