What is the role of の in this sentence?

質問を翻訳

トイレに入るとき、部屋で履いているスリッパのまま入ってはいけない。

I'm practicing parsing sentences in Japanese to fully immerse myself in the grammatical functions of each part. I got:

- トイレ - bathroom
- に - action location marker
- 入る - to enter, dictionary form
- とき - during, the time of, when
- 部屋 - room
- で - physical location marker
- 履いている - wearing
て-form (connecting actions) of 履く
て-form + いる = ___-ing; ongoing action
- スリッパ - slippers
- の - ??
- まま - as it is, this state, with
- 入ってはいけない - must not enter
て-form (connecting actions) of 入る【はいる】
て-form + はいけない = must not do...

I managed to clean this up to: "When entering the bathroom, do not wear the slippers you're wearing in the room."

I'm just not understanding what role の played in this one. Feel free to pick apart with me or correct anything I misunderstood.

Thanks for any help!