The MathNet Korea
Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Glasnik Matematicki Serja III.
( Vol. 34 NO.2 / (1999))
Parabolic Induction and Jacquet Modules of Representations of $O(2n,F)$
Dubravka Ban,
Pages. 147-185
Abstract For the sum of the Grothendieck groups of the categories of smooth finite length representations of $O(2n,F)$ (resp., $SO(2n,F)$), $n geq 0$, ($F$ 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
$GL(n,F), ; n geq 0$, 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 the comodule structures, is obtained.
Contents 1. Introduction 2. Preliminaries 3. General linear group 4. Special orthogonal group $SO(2n,F)$ 5. Calculations in the root system, the case of $D_n$ 6. Orthogonal group $O(2n,F)$ 7. Jacquet modules of induced representations for $O(2n,F)$
Key words representations of p-adic groups, enen orthogonal groups, special even orthogonal groups, parabolic induction, Jacquet modules
Mathmatical Subject Classification 20G05, 22E50