On induced representations. (Russian) Zbl 0714.22014

Bott, R.

Usp. Mat. Nauk 45, No. 3(273), 85-96 (1990).

A Russian translation of the talk at the conference “The mathematical heritage of H. Weyl” [Proc. Symp. Pure Math. 48, 1-13 (1988; Zbl 0657.22020)]. After telling about his contacts with H. Weyl the author outlines the development of the theory of induced representations starting with the classical Weyl character formula.

Reviewer: A.L.Onishchik

MSC:

22E65	Infinite-dimensional Lie groups and their Lie algebras: general properties
22E46	Semisimple Lie groups and their representations
01A70	Biographies, obituaries, personalia, bibliographies
58D15	Manifolds of mappings
14F40	de Rham cohomology and algebraic geometry
58A14	Hodge theory in global analysis

Keywords:

irreducible representations; semisimple compact Lie group; Borel-Weil- Bott theorem; holomorphic sections; Atiyah-Bott-Lefschetz formula; homogeneous space; coadjoint action; Loop groups; H. Weyl; induced representations; Weyl character formula

Citations:

Zbl 0638.22009; Zbl 0618.22011; Zbl 0657.22020