Elijah the Prophet is Pinchas, (Zohar) who had the nefesh zehira ila’a of Adam. Therefore, Nadab and Abihu came into him in ibur in the incident with Zimri, since they were also the level of the nefesh of Adam from the aspect of the nefesh of Asiya, as mentioned earlier.

Likes attract and aid each other to rectify.

Nadab and Abihu had to die through burning.

Now, had the Jewish people not sinned with the [golden] calf, the zuhama would have been completely removed from them.1 Had that been the case, then even though Nadab and Abihu sinned with the incense, they could have simply died a normal death. However, since Israel did commit the sin with the calf, they caused the zuhama to adhere once again to the nefesh of Adam. As a result, Nadab and Abihu had to die through burning.

Before the sin, Adam’s body was from the world of Yetzira. The sin caused a great fall to the lowly, earthy realm of Asiya and the body assumed a base, physical attire. (Likutei Torah, Bereishit) This is what the snake has a hold on. Physically, man is not that much different than beast.2

Fire destroys the substantiality of the material. It is therefore one method of destroying the evil energy of the snake intermingled with the body. Cremation is forbidden as G‑d in His infinite wisdom sees that the best rectification for the body after death is to let it deteriorate. Therefore, only their souls were burned while their bodies were left unscathed, for the negative energy was primarily attached to their souls and from there was burned away. Their bodies were buried and left to natural designs.

This is the reason for, "And all your brothers the entire House of Israel shall cry over the burning." (Lev. 10:6) Their sin of the [golden] calf caused the burning of the nefesh of Adam, the father of the entire world. This is the reason why Nadab and Abihu were considered equal to the entire Jewish people, like Moses and Aaron, because they possessed the nefesh of Adam itself.

Rashi states that Moses remarked to Aaron that he knew the consecration of the Tabernacle would involve the death of great tzadikim. He had thought that it would be himself or Aaron. After Nadab and Abihu were taken, he saw that they were greater.

Even though we explained that in order to draw down the tremendous Shechinah concentration in the Tabernacle, it was necessary to create an extreme awakening from below, which was to come through tzadikim dying for the Divine honor. Still, if they had not sinned with the golden calf, it would have been possible to make this awakening by means of the offerings without anyone having to die.3

After the golden calf, only the choicest were powerful enough...

After the golden calf, only the choicest were powerful enough to propel a strong enough ascent from below to bring down the highest light. This shows the greatness of Nadab and Abihu. The secret is here revealed – that they are from the nefesh of Adam himself.

Adam’s mistake took the Shechinah out of the universe, he himself is accordingly the one to sacrifice and give up life for its return.

Regarding the ibur into Pinchas it is written, "Remember NA/na [please] which NKI/naki [innocent] person ever perished," (Job 4:7) as the Zohar says. (Pinchas 217a) For the first letters of Nadab and Abihu are NA/nun-aleph, and they are from the root of KYN/Cain, whose letters spell NKY/naki. In other words, they never perished but went into Pinchas, who was also from Cain. However, as we explained earlier, (Chapter 32) when Pinchas sinned with the incident of the daughter of Yiftach, the ibur of Nadab and Abihu was removed from him and it went to Samuel the Prophet.

Above, the Ari'Zl taught us that NA/na hints to Nadav and Abihu, when this word of supplication was used by Elisha to receive double the spirit of Elijah. It again comes into play here by the verse speaking of Pinchas/Elijah receiving these souls to fix them.

Above we explained that na ['please'] fixes the forceful taking of light found in the Cain root in Tohu. Two na’s are necessary to fully repair this: one at the stage of Pinchas himself receiving the souls and one when he passed them on as Elijah to Elisha.4

As a result of Israelites sinning with the Moabite women, a plague was sent and they were dying like flies. Pinchas got up, was vengeful on behalf of G‑d, killed the main offenders, and the plague ceased. (Num. 25:1-9) His jealousy for the Divine honor fixed Cain's selfish jealousy. By saving his brethren from deserved death, Pinchas fixed Cain’s killing his brother undeservedly. His care about his brothers fixed Cain’s "Am I my brother’s keeper?"(Gen. 4:9)

Pinchas thus rectified the separateness and lack of relation of the sefirot of Tohu...

At first the sefirot of Tohu were selfish in that each one received directly from Ein Sof, without giving to each other. Then the vessels tried to obtain too much light. (Eitz Chayim, Shaar Shevirat HaKeilim) Pinchas thus rectified the separateness and lack of relation of the sefirot of Tohu, source of the Cain mechanics. This gave into Pinchas’ jurisdiction the choice souls of Cain.

Korach the son of Yitzhar was from the level of the ruach of Cain from the side of evil, as the verse indicates, "And Korach took" (Num. 16:1) - see the Targum there.5 This evil ruach of Cain was enclothed within him [Korach], and therefore he accused Abel his brother, [who was enclothed in] Moses. However Jethro, though he too is from Cain, as it says, "Heber the Kenite separated from KYN/Kenites," (Judges 4:11) is from the level of good of Cain. Therefore, he gave his daughter Tziporah to Moses, was good to him, and fed him bread.

This greatly fixed the Cain root. Empowered by it, Jethro ’s recognizing one G‑d and His power was actually the local catalyst for the giving of the Torah. (Zohar, see Likutei Moharan 10) The crown of Torah goes together with the others, which belong to Cain the firstborn.

Korach thought he had rectified Cain the firstborn, and therefore he tried to overcome Moses, who was Abel. However, he had erred in this because the tikun of Cain could not have come through Korach, since he was from his evil side. Rather, it could only come through his descendant, Samuel the Prophet, who was also from the good side of Cain. The Sages have said that Korach prophesized but did not know [what he was prophesying], because he saw a fire go out from his [reproductive] organ [making him think that since his descendents were to be rulers,6 he would be successful in usurping Moses7]. Understand this.

[Translation and commentary by Perets Auerbach.]