The local Langlands correspondence for GL_n

A thirteen-lesson course connecting representations of general linear groups over local fields with Weil–Deligne parameters. It covers the real correspondence, representation classification, local factors and the converse theorem, monodromy blocks, explicit rank-two factor matching, dihedral supercuspidals and rectifiers, modular forms and CM elliptic curves, inner forms and Jacquet–Langlands, existence strategies, base change, induction and formal degrees, and parameters and packets for reductive groups. Proofs and complete exercise solutions accompany the explicit calculations; deep existence and classification theorems are stated with precise references.

1. First cases: characters and the real correspondence (in preparation)
2. Irreducible representations of general linear groups over a local field
3. Local factors of pairs and the rank-two converse theorem
4. The statement of the local Langlands correspondence
5. Monodromy blocks and the passage from supercuspidals to all parameters
6. The rank-two correspondence: principal series, Steinberg twists and characters
7. Two-dimensional Weil representations: induction and projective symmetry
8. Dihedral supercuspidals, rectifiers and rank-two characterization
9. Modular forms, elliptic curves and local–global compatibility
10. Jacquet–Langlands: elliptic classes and division-algebra representations
11. Harris–Taylor: geometry, numerical counting and existence
12. Other proofs, functoriality and the formal-degree formula
13. Beyond general linear groups: parameters and packets

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