Deep learning methods, including Convolutional Neural Networks, Transformers and Mamba, have achieved remarkable success in hyperspectral image (HSI) classification. Nevertheless, existing methods exhibit inflexible integration of local-global representations, inadequate handling of spectral-spatial scale disparities across heterogeneous bands, and susceptibility to the Hughes phenomenon under high-dimensional sample heterogeneity. To address these challenges, we propose Local-Global Expert Spatial-Spectral Transformer (LGEST), a novel framework that synergistically combines three key innovations. The LGEST first employs a Deep Spatial-Spectral Autoencoder (DSAE) to generate compact yet discriminative embeddings through hierarchical nonlinear compression, preserving 3D neighborhood coherence while mitigating information loss in high-dimensional spaces. Secondly, a Cross-Interactive Mixed Expert Feature Pyramid (CIEM-FPN) leverages cross-attention mechanisms and residual mixture-of-experts layers to dynamically fuse multi-scale features, adaptively weighting spectral discriminability and spatial saliency through learnable gating functions. Finally, a Local-Global Expert System (LGES) processes decomposed features via sparsely activated expert pairs: convolutional sub-experts capture fine-grained textures, while transformer sub-experts model long-range contextual dependencies, with a routing controller dynamically selecting experts based on real-time feature saliency. Extensive experiments on four benchmark datasets demonstrate that LGEST consistently outperforms state-of-the-art methods.