Orbits of groups generated by transvections over F-2

Let V be a finite dimensional vector space over the two element field. We compute orbits for the linear action of groups generated by transvections with respect to a certain class of bilinear forms on V. n particular, we compute orbits that are in bijection with connected components of real double Bruhat cells in semisimple groups, extending results of M. Gekhtman, B. Shapiro, M. Shapiro, A. Vainshtein and A. Zelevinsky.


Galois structure of modular forms of even weight
Gurel, E. (Elsevier BV, 2009-10-01)
We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.
Curves with many points and configurations of hyperplanes over finite fields
Özbudak, Ferruh (Elsevier BV, 1999-10-01)
We establish a correspondence between a class of Kummer extensions of the rational function field and configurations of hyperplanes in an affine space. Using this correspondence, we obtain explicit curves over finite fields with many rational points. Some of our examples almost attain the Oesterle bound. (C) 1999 Academic Press.
Value sets of Lattes maps over finite fields
Küçüksakallı, Ömer (Elsevier BV, 2014-10-01)
We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic case. We determine the value sets of Lattes maps over finite fields which are rational functions induced by isogenies of elliptic curves with complex multiplication.
On maximal curves and linearized permutation polynomials over finite fields
Özbudak, Ferruh (Elsevier BV, 2001-08-08)
The purpose of this paper is to construct maximal curves over large finite fields using linearized permutation polynomials. We also study linearized permutation polynomials under finite field extensions.
Khrebtova, Ekaterina S.; Malinin, Dmitry (World Scientific Pub Co Pte Lt, 2008-12-01)
We prove the existence and finiteness theorems for integral representations stable under Galois operation. An explicit construction of the realization fields for representations of finite groups stable under the natural operation of the Galois group is given. We also compare the representations over fields and the rings of integers, and give a quantitative result on the rarity of integral Galois stable representations. There is a series of related conjectures and applications to arithmetic algebraic geometr...
Citation Formats
A. İ. Seven, “Orbits of groups generated by transvections over F-2,” JOURNAL OF ALGEBRAIC COMBINATORICS, pp. 449–474, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35225.