Glumly is how you do something when you are glum: unhappily, with little talk, and with that heavy, fallen look. You walk glumly, nod glumly, or say something glumly — the adverb hangs on the action, not on the person. It has the same slightly old, slightly British colour as glum. It does not mean slowly, and it does not mean angrily. It means the quiet unhappy feeling is sitting on the way you act. Though actually, people often choose a plainer word in speech (sadly, quietly) and keep glumly for writing, or for a small joke when someone is making a long face.