Broadcasting sparse matrices

I have a (dense) Tensor X of shape (A, B, C) that I need to (tensor-)multiply with a sparse tensor Y of shape (C,C) along the last axis of the X and first axis of Y independently of the first two axes of X to create a new Tensor of shape (A, B, C). How do I appropriately broadcast Y? I definitely need to avoid looping over the first two axes of X.