As it happens, TiB, this is something that is currently playing out in the Depute Leadership competition. The newly enfranchised left wing of the SNP have their candidate in former Scottish Labour apparatchik Tommy Sheppard . For years the SNP has talked a far more left wing game than it walked; however with the post referendum membership bonanza they now have a membership more eager to walk that walk.
This is a list of all of the other candidates. My apologies for using Yoon media 
I would guess that either Westminster terrier Angus Robertson or speecifying MEP Alyn Smith would be the prefered candidates of the SNP establishment.
I think any conflict between the SNP's left and right wings is being smothered by the fact that they are in government in Scotland. Success does more to quieten grumbles than most. A double achievement considering the fact that the SNP has a genuine right wing. As apposed to the Labour Party for whom right-wing is a catty, but successful, branding of centrists by the hard left. I don't think these fracture lines will be seen in the SNP (regardless of who wins the election) until the party's fortunes start to suffer.
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