Who are the critical partners/stakeholders in the organization for industry PMM?

Other than everyone? 

Product and UX - To highlight industry-specific opportunities for roadmap or positoning

Sales - To help them drive better discovery, solution positioning, and credibility with a customer

PMM - To pressure test messaging and inherit the best, most compelling value props they have

Customer Success - drive renewals and critical vertical customer stories to drive growth

Execs - You need great storytellers who "love" your vertical, even if they're not deep. 

Demand Gen - To make sure you're properly targeting and communicating with vertical buyers

First and foremost is the industry sales team. Usually industry PMMs have sales teams that are also mapped to a particular industry. Sometimes there’s also verticalized pre-sales or post sales teams that the PMMs work closely with. 

Second is the industry specialists team. This team usually has deep industry or functional expertise and are great thought partners with PMMs on a variety of GTM motions. It can be collaborating on messaging, pitch decks, speaking sessions and developing the key use cases. 

Third is the rest of the marketing team. Industry PMMs are internal SMEs for the rest of the marketing org to understand the key personas, use cases, top customers, key publishers/conferences where we can reach these audiences, and work with the cross-functional marketing partners to develop the overall marketing strategies and campaigns.