scholarly journals Finding hidden Borel subgroups of the general linear group

2012 ◽  
Vol 12 (7&8) ◽  
pp. 661-669
Author(s):  
Gabor Ivanyos
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
Quantum Algorithm ◽  
General Linear ◽  
Base Field ◽  
Triangular Matrices ◽  
Hidden Subgroup Problem ◽  
Subgroup Problem ◽  
Lower Triangular ◽  
Lower Triangular Matrices

We present a quantum algorithm for solving the hidden subgroup problem in the general linear group over a finite field where the hidden subgroup is promised to be a conjugate of the group of the invertible lower triangular matrices. The complexity of the algorithm is polynomial when size of the base field is not much smaller than the degree.

Conjugacy classes of torsion in GL_n(Z)

2015 ◽  
Vol 30 ◽  
Author(s):  
Qingjie Yang
Keyword(s):  
Linear Group ◽  
Equivalence Relation ◽  
General Linear Group ◽  
Conjugacy Classes ◽  
Complete List ◽  
General Linear ◽  
Triangular Matrices ◽  
Torsion Element ◽  
Ring Of Integers

The problem of integral similarity of block-triangular matrices over the ring of integers is connected to that of finding representatives of the classes of an equivalence relation on general integer matrices. A complete list of representatives of conjugacy classes of torsion in the 4 × 4 general linear group over ring of integers is given. There are 45 distinct such classes and each torsion element has order of 1, 2, 3, 4, 5, 6, 8, 10 or 12.

scholarly journals A Plethysm Formula on the Characteristic Map of Induced Linear Characters from $U_n(\mathbb F_q)$ to $GL(\mathbb F_q)$

10.37236/2364 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
Zhi Chen
Keyword(s):  
Finite Field ◽  
Recurrence Relation ◽  
Linear Group ◽  
General Linear Group ◽  
Symmetric Functions ◽  
General Linear ◽  
Triangular Matrices ◽  
Upper Triangular Matrices ◽  
Characteristic Map

This paper gives a plethysm formula on the characteristic map of the induced linear characters from the unipotent upper-triangular matrices $U_n(\mathbb F_q)$ to $GL_n(\mathbb F_q)$, the general linear group over finite field $\mathbb F_q$. The result turns out to be a multiple of a twisted version of the Hall-Littlewood symmetric functions $\tilde{P}_n[Y;q]$. A recurrence relation is also given which makes it easy to carry out the computation.

scholarly journals Some subordination involving polynomials induced by lower triangular matrices

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Saiful R. Mondal ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Unit Disk ◽  
Triangular Matrices ◽  
Cesàro Mean ◽  
Cesaro Mean ◽  
Lower Triangular ◽  
Lower Triangular Matrices

Abstract The article considers several polynomials induced by admissible lower triangular matrices and studies their subordination properties. The concept generalizes the notion of stable functions in the unit disk. Several illustrative examples, including those related to the Cesàro mean, are discussed, and connections are made with earlier works.

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
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