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Hyperspectral image (HSI) classification has become a popular research topic in recent years, and transformer-based networks have demonstrated superior performance by analyzing global semantic features. However, using transformers for pixel-level HSI classification has two limitations: ineffective capture of spatial-spectral correlations and inadequate exploitation of local features. To address these challenges, we propose a dual-dimension self-attention (D²SA) mechanism that fully exploits HIS's high spectral-spatial correlation by using two separate branches to model the global dependence of features from the spectral and spatial dimensions. Additionally, we develop a multilayer residual convolution module that extracts local features and introduces shallow-deep feature interactions to obtain more discriminative representations. Based on these components, we propose a dual-dimension spectral-spatial bottleneck transformer (D²S²BoT) framework for HSI classification that simultaneously models the local interactions and global dependencies of HSI pixels to achieve high-precision classification. By virtue of the D²SA mechanism, the introduced D²S²BOT framework can produce competitive classification results with a limited number of training samples on three well-known datasets, which we hope will provide a strong baseline for future research on transformers in the field of HSI.