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Geometric quantization and derived functor modules for semisimple Lie groups by Wilfried Schmid; Joseph A Wolf is a Mathematics article available to read on EtoBox.

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AND JOSEPH A. WOLLT' l.et Ci he a semisimple Lie group. $1 the complexified Lie algchra, and X the flag variety of g. The mechanism of geometric quantization suggests that the various G-orbits in X should give rise to representations of G. On the other hand, Znckerman's derived functor constructton attacks algebraic representations of g to G-orbits. In this paper we show that geometric quantizafion leads to Frkchet representations of finite length, which are the maximal globalizations of the derived fnnctor modules. We give two alternate realizations of the representations, as cohomology spaces of Th complexes with hypcrfunction cocfkents. and as local co~~o~~lffio~y groups along G-orbits in S. We use the latter realization to implement the duality between the derived functor modules and the Beilinson 3ernstein modules, as cup product between local ~ohornoi~~~y grrtup followed by eva~uatj~)~l over the fundamental cycle. ( / YW hcadrmrr Pms. IIlL H\*(C"(G/H; E@ A'N\*), d,,) that results in Harish Chandra modules for G. Let -&'(t-~, K)(,, denote the category of K-finite (9, K)-modules, .J.@'(~, Hn f%,, K, the same thing with K replaced by H n K, and I': .N(g, Hn K) ,,,, ~k,-~l/(n, KY

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Author

Wilfried Schmid; Joseph A Wolf

Publisher

Elsevier BV

Published

1990

Language

EN

Field

Mathematics (Physical Sciences)