Locally Mixed Symmetric Spaces

This chapter introduces the notion which is main interest in this book and responsible for title. Locally mixed symmetric spaces are a very natural construction enrich of locally spaces, studied Chap. 2. While there pair data entering, \((G_{\mathbb Q}, {\varGamma })\), where \(G_{\mathbb Q}\) semisimple \({\mathbb Q}\)-group such that \(X=G_{\mathbb R}/K\) space non-compact type maximal compact subgroup \(K\subset G_{\mathbb R}\) \( }\subset an arithmetic group, now triple defining situation: },{\boldsymbol{\rho }})\), \({\boldsymbol{\rho }}:G_{\mathbb Q}\longrightarrow GL(V)\) faithful rational representation (not necessarily defined over Q}\)).