Représentations de Weil et GL2. Algèbres de division et GLn : vers les corps de classes galoisiens I, II / Tetsuo Kaise

This book is written in an unusual style; the modern standards like "a mathematical formula should be displayed'', which are very convenient for the reader who wishes to get an overview of the book quickly, are not followed and made the reviewer's task of reading the book difficult.
The first part of the book concerns the construction and the relation between the irreducible local representations of GL(2) and the multiplicative group of a quaternion algebra, over a local non-Archimedean local field F—including the case of characteristic 2. The method is entirely local. The second part concerns the construction and the relation between the irreducible square-integrable representations of GL(n) and the multiplicative group G of a division algebra over F. The results announced in the first part are nowadays well known, and are proved by different but similar methods. But the results announced for GL(n,F) are new: the construction is new, and the proof of the relation between the representations of G and GL(n,F) is new. One of the ideas is to embed these two groups in GL(n,L) where L/F is the unramified extension of degree n of F. (MathSciNet)