Cross-domain sequential recommendation (CDSR) aims to uncover and transfer users' sequential preferences across multiple recommendation domains. While significant endeavors have been made, they primarily concentrated on developing advanced transfer modules and aligning user representations using self-supervised learning techniques. However, the problem of aligning item representations has received limited attention, and misaligned item representations can potentially lead to sub-optimal sequential modeling and user representation alignment. To this end, we propose a model-agnostic framework called \textbf{C}ross-domain item representation \textbf{A}lignment for \textbf{C}ross-\textbf{D}omain \textbf{S}equential \textbf{R}ecommendation (\textbf{CA-CDSR}), which achieves sequence-aware generation and adaptively partial alignment for item representations. Specifically, we first develop a sequence-aware feature augmentation strategy, which captures both collaborative and sequential item correlations, thus facilitating holistic item representation generation. Next, we conduct an empirical study to investigate the partial representation alignment problem from a spectrum perspective. It motivates us to devise an adaptive spectrum filter, achieving partial alignment adaptively. Furthermore, the aligned item representations can be fed into different sequential encoders to obtain user representations. The entire framework is optimized in a multi-task learning paradigm with an annealing strategy. Extensive experiments have demonstrated that CA-CDSR can surpass state-of-the-art baselines by a significant margin and can effectively align items in representation spaces to enhance performance.