Existing architectures of multi-domain learning have two types of adapters: shared LoRA for all domains and domain-specific LoRA for each particular domain. However, it remains unclear whether this structure effectively captures domain-specific information. In this paper, we propose a method that ensures that shared and domain-specific LoRAs exist in different subspaces; specifically, the column and left null subspaces of the pre-trained weights. We apply the proposed method to action recognition with three datasets (UCF101, Kinetics400, and HMDB51) and demonstrate its effectiveness in some cases along with the analysis of the dimensions of LoRA weights.