scholarly journals Constructing projective varieties in weighted flag varieties II

2015 ◽  
Vol 158 (2) ◽  
pp. 193-209 ◽  
Author(s):  
MUHAMMAD IMRAN QURESHI
Keyword(s):  
Linear Group ◽  
Lie Group ◽  
General Linear Group ◽  
Hilbert Series ◽  
Flag Variety ◽  
General Linear ◽  
Flag Varieties ◽  
Projective Varieties

AbstractWe give the construction of weighted Lagrangian GrassmannianswLGr(3,6) and weighted partialA3flag varietywFL1,3coming from the symplectic Lie group Sp(6, ℂ) and the general linear group GL(4, ℂ) respectively. We give general formulas for their Hilbert series in terms of Lie theoretic data. We use them as key varieties (Format) to construct some families of polarized 3-folds in codimension 7 and 9. Finally, we list all the distinct weighted flag varieties in codimension (4 ⩽c⩽ 10.

scholarly journals BOUNDEDNESS PROPERTIES OF AUTOMORPHISM GROUPS OF FORMS OF FLAG VARIETIES

2020 ◽  
Vol 25 (4) ◽  
pp. 1161-1184
Author(s):  
A. GULD
Keyword(s):  
Automorphism Group ◽  
Linear Group ◽  
General Linear Group ◽  
Automorphism Groups ◽  
Finite Subgroup ◽  
Flag Variety ◽  
General Linear ◽  
Roots Of Unity ◽  
Flag Varieties ◽  
Projective General Linear Group

Abstract We call a flag variety admissible if its automorphism group is the projective general linear group. (This holds in most cases.) Let K be a field of characteristic 0, containing all roots of unity. Let the K-variety X be a form of an admissible flag variety. We prove that X is either ruled, or the automorphism group of X is bounded, meaning that there exists a constant C ∈ ℕ such that if G is a finite subgroup of AutK(X), then the cardinality of G is smaller than C.

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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