Original scientific paper

Parabolic induction and Jacquet modules of representations of O(2n,F)

Dubravka Ban

Abstract

For the sum of the Grothendieck groups of the categories of smooth finite length representations of O(2n, F) (resp., SO(2n, F)), n ≥ 0, (F a p-adic field), the structure of a module and a comodule over the sum of the Grothendieck groups of the categories of smooth finite length representations of GL(n, F), n ≥ 0, is achieved. The multiplication is defined in terms of parabolic induction, and the comultiplication in terms of Jacquet modules. Also, for even orthogonal groups, the combinatorial formula, which connects the module and comodule structures, is obtained.

Keywords

Representations of p-adic groups; even orthogonal groups; special even orthogonal groups; parabolic induction; Jacquet modules

Hrčak ID:

6411

URI

https://hrcak.srce.hr/6411

Publication date:

1.12.1999.

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