An Efficient Quantum Algorithm for Finding Hidden Parabolic Subgroups in the General Linear Group

@inproceedings{Decker2014AnEQ,
title={An Efficient Quantum Algorithm for Finding Hidden Parabolic Subgroups in the General Linear Group},
author={T. Decker and G. Ivanyos and Raghav Kulkarni and Y. Qiao and M. Santha},
booktitle={MFCS},
year={2014}
}

In the theory of algebraic groups, parabolic subgroups form a crucial building block in the structural studies. In the case of general linear groups over a finite field \(\mathbb{F}_q\), given a sequence of positive integers n 1, …, n k , where n = n 1 + … + n k , a parabolic subgroup of parameter (n 1, …, n k ) in GL\(_n(\mathbb{F}_q)\) is a conjugate of the subgroup consisting of block lower triangular matrices where the ith block is of size n i . Our main result is a quantum algorithm of… CONTINUE READING