I couldn't find anything specific regarding Jumuah but hope this helps
Ahadeeth:
1) Abu Saeed Khudri (RA) relates that Rasul-ullah (SAW) said, “ if there are three people, then one should be the Imam, and the person who is the most “AQRA” (the one who reads the most) has the right to be the Imam.
(Bukhari and Muslim).
2) Ibn-Masud (RA) relates that Rasul-ullah (SAW) said, “ A person should become the Imam of people who is the most “AQRA” amongst them. If all are equal then the one who has the most knowledge of Sunnah. If they are equal in knowledge of the Sunnah then the one who made Hijrah (migration) first. If they are equal in regards to hijrah then the most who is the oldest. And NO ONE should perform Imamat in place of an individual; and one SHOULD NOT sit in some one else’s house (at their place of sitting i.e. the owner’s place of sitting) without seeking permission.
(Ahmed, Muslim)
Opinion of the Fuqaha:
1) According to Imam Abu Haneefa (RA) a person who is the most “AQRA” (the one who reads the most i.e. a Hafiz) is superior to the one who is “AFQA” (the one who has the most knowledge of Sunnah i.e a scholar); as mentioned in the two Ahadeeth mentioned above.
2) According to Imam Abu Ahmad Bin Hanbal (RA) a person who is the most “AQRA” (the one who reads the most i.e. a Hafiz) is superior to the one who is “AFQA” (the one who has the most knowledge of Sunnah i.e a scholar); as mentioned in the two Ahadeeth mentioned above.
Imam Nawawi (RA) writes, “ The words of the Hadeeth say that if they are equal in reading then the one who has the most knowledge of the Sunnah. This is the Daleel that “AQRA” is superior to “AFQA”.
3) According Imam Shafa’e (RA) for Imamat an “AFQA” is better then “AQRA”.
4) According to Imam Malik (RA) for Imamat as “AFQA” is better then “AQRA”.
Imam Shafa’e (RA) states, “This Hadeeth was addressed to the Sahaba (RA).
Amongst the Sahaba the person who used to read the most was accepted as the one who knew the most. The Sahaba (RA) accepted Islam at an older age. Therefore they used to understand first before reading. There were NONE amongst Sahaba who could read but NOT understand, but there were some who could understand but NOT read.
Source: Nael-ul-Awtar :Vol3, Pg133
Fatwa of Hanafi Scholars of Deoband:
1) Imamat is the right of one who is superior in knowledge, because:
a) Rasul-ullah (SAW) in his last days appointed Abu Bakr (RA) as the Imam, despite his own saying that Kaa’b (RA) is the best Qari (reciter) of the Qua’an (Bukhari).
b) Imam Bukhari (RA) has titled the chapter containing the above Hadeeth as “The one with superior Ilm (knowledge) and Fadhl has more right of Imamat”.
According to the Shar’h of Qudoori (taught in the Hanafi Darul-ulooms), the opinion mentioned in “opinion of the Fuqaha” is of Imam Abu Yusuf (RA); the student of Imam Abu Haneefa (RA).
WHO SHOULD NOT BE THE IMAM?
Hadeeth:
1) Abdullah Bin Umar (RA) narrates that Rasul-ullah (SAW) said, “Allah does NOT accept the prayer (Namaz) of three individuals:
a) One is the person who performs Imamat of people who don’t like him.
b) Second is the person who comes for prayer (Namaz) when the time is finishing.
c) Third is the person who frees a slave and then enslaves him again.
(Abu Dau’d, Ibn-e-Maja)
Opinion of Muhaditheen:
1) Imam Tirmidhi (RA) writes, “From amongst the Sahaba (RA) some have disliked for a person to do Imamat of people that don’t like him. But if the Imam is NOT an oppressor then the people who don’t like him will be sinful.
Opinion of Fuqaha:
1) There is a consensus of all Madhabs on the issue mentioned above.
Source: (Al-Fiqh Vol1, pg383)
Note: Please note that I think this might be a misprint and the actual page number should be 283 to be consistent with all other references from the same Book on the same subject).
Ahadeeth:
1) Abu Huraira (RA) narrates that Rasul-ullah (SAW) said, “It is Waajib for you to join an Ameer and wage Jihad whether he is pious or NOT, similarly it is Waajib for you to pray behind every Muslim whether he is pious or NOT eventhough he might be committing major sins.
(Abu Da’ud)
2) Abu Huraira (RA) narrates that Rasul-ullah (SAW) said, “Read Salah behind every person who proclaims ‘La Ilaha Ilullah’ and read the Janazah of every person who proclaims ‘La Ilaha Ilullah’.
(Dar Qutni)
Both of the above Ahadeeth are weak, but are substantiated by the actions of the Sahaba (RA), and also by the two Ahadeeth mentioned below.
3) Ibn-e-Umar (RA) used to perform Salah behind Hajjaj.
(Bukhari)
4) Abu Saeed Khudri (RA) performed Eid Salah behind Mirwan, even though Mirwan was the man who performed the Khutbah of Eid before Salah.
(Muslim, Abu Dau’d, Tirmidhi)
Opinion of the Fuqaha:
1) According to Imam Haneefa (RA) Imamat of a Faasiq (sinner) is Makrooh.
2) According to Imam Ahmad Bin Hanbal (RA) Imamat of a Faasiq (sinner) is NOT permissible.
3) According to Imam Shafa’e (RA) Imamat of a Faasiq (sinner) is Makrooh.
4) According to Imam Malik (RA) Imamat of a Faasiq (sinner) is Makrooh.
Source (Fiqh Ala Madhahib Arba: Vol1: pg283)
5) According to Imam Shawkani (RA) the difference of opinion is whether prayer (Salah) is valid behind a person who is a Faasiq (sinner) and an oppressor.