Automorphic Representations and L-Functions for the General Linear Group

2009 ◽  
Author(s):  
Dorian Goldfeld ◽  
Joseph Hundley
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
General Linear ◽  
Automorphic Representations

Representations induced from the Zelevinsky segment and discrete series in the half-integral case

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ivan Matić
Keyword(s):  
Linear Group ◽  
Local Field ◽  
General Linear Group ◽  
Discrete Series ◽  
Series Representation ◽  
General Linear ◽  
Composition Series ◽  
Induced Representations ◽  
Discrete Series Representation

AbstractLet {G_{n}} denote either the group {\mathrm{SO}(2n+1,F)} or {\mathrm{Sp}(2n,F)} over a non-archimedean local field of characteristic different than two. We study parabolically induced representations of the form {\langle\Delta\rangle\rtimes\sigma}, where {\langle\Delta\rangle} denotes the Zelevinsky segment representation of the general linear group attached to the segment Δ, and σ denotes a discrete series representation of {G_{n}}. We determine the composition series of {\langle\Delta\rangle\rtimes\sigma} in the case when {\Delta=[\nu^{a}\rho,\nu^{b}\rho]} where a is half-integral.

scholarly journals Euler equations on the general linear group, cubic curves, and inscribed hexagons

2016 ◽  
Vol 62 (1) ◽  
pp. 143-170
Author(s):  
Konstantin Aleshkin ◽  
Anton Izosimov
Keyword(s):  
Euler Equations ◽  
Linear Group ◽  
General Linear Group ◽  
General Linear ◽  
Cubic Curves

Parabolic extensions of a Hecke ring of the general linear group

1988 ◽  
Vol 43 (4) ◽  
pp. 2533-2540 ◽  
Author(s):  
V. A. Gritsenko
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
General Linear

scholarly journals Products of reflections in the general linear group over a division ring

1979 ◽  
Vol 28 ◽  
pp. 53-62 ◽  
Author(s):  
Dragomir Z̆. Djoković ◽  
Jerry Malzan
Keyword(s):  
Linear Group ◽  
Division Ring ◽  
General Linear Group ◽  
General Linear

scholarly journals Triple factorisations of the general linear group and their associated geometries

2015 ◽  
Vol 469 ◽  
pp. 169-203 ◽  
Author(s):  
Seyed Hassan Alavi ◽  
John Bamberg ◽  
Cheryl E. Praeger
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
General Linear

Two-Dimensional Linear Groups Over Local Rings

1969 ◽  
Vol 21 ◽  
pp. 106-135 ◽  
Author(s):  
Norbert H. J. Lacroix
Keyword(s):  
Local Ring ◽  
Linear Group ◽  
General Linear Group ◽  
General Linear ◽  
Linear Groups ◽  
Local Rings ◽  
Two Dimensional ◽  
Normal Subgroups ◽  
Field Case

The problem of classifying the normal subgroups of the general linear group over a field was solved in the general case by Dieudonné (see 2 and 3). If we consider the problem over a ring, it is trivial to see that there will be more normal subgroups than in the field case. Klingenberg (4) has investigated the situation over a local ring and has shown that they are classified by certain congruence groups which are determined by the ideals in the ring.Klingenberg's solution roughly goes as follows. To a given ideal , attach certain congruence groups and . Next, assign a certain ideal (called the order) to a given subgroup G. The main result states that if G is normal with order a, then ≧ G ≧ , that is, G satisfies the so-called ladder relation at ; conversely, if G satisfies the ladder relation at , then G is normal and has order .

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