arXiv:2605.21987v2 Announce Type: replace Abstract: Recent conversational recommender systems have begun to unify recommendation and response generation within autoregressive models, with semantic IDs providing a natural representation for generative recommendation. However, relational knowledge is typically organized around item-level representations, which do not naturally align with the compositional SIDs. This mismatch makes it difficult for unified CRSs to effectively exploit structured catalog relations. We propose HGCRS, a hypergraph-enhanced generative conversational recommender system that bridges this gap with an SID--entity hypergraph. Each item forms a hyperedge connecting its SID codes and attribute entities, and a type-aware hypergraph encoder incorporates relational information into generative item selection. HGCRS further introduces a mode--item--response protocol for jointly modeling recommendation-bearing and response-only turns. Experiments on ReDial and INSPIRED demonstrate strong recommendation performance while maintaining competitive response generation quality.