Naslov
Some unexpected phenomena in the Franke filtration of the space of automorphic forms of the general linear group

Autori
Grbac, Neven ; Grobner, Harald

Vrsta, podvrsta
Radovi u časopisima, znanstveni

Izvornik
Israel journal of mathematics (2022)

Status rada
Prihvaćen

Ključne riječi
automorphic forms ; automorphic representations ; Franke filtration ; Eisenstein series ; general linear group

Sažetak
In his famous paper [11], J. Franke has defined a certain finite filtration of the space of automorphic forms of a general reductive group, which captures most of its internal representation theory. The purpose of this paper is to provide several concrete examples of yet unexpected phenomena, which occur in the Franke filtration for the general linear group. More precisely, we show that the degenerate Eisenstein series arising from the parabolic subgroups of the same rank are not necessarily contributing to the same quotient of the filtration, and that, even more, the Eisenstein series arising from the parabolic subgroups of higher relative rank may contribute to a deeper quotient of the filtration. These are the first structural counterexamples to an expectation, mentioned in [11].

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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