Related papers: Total positivity in reductive groups, II
This is a preliminary version of the first chapter of a book project on the character theory of finite groups of Lie type. It provides the foundations from the general theory of reductive algebraic groups over a finite field.
In this manuscript, we define the notion of linearly reductive groups over commutative unital rings and study the Cohen-Macaulay property of the ring of invariants under rational actions of a linearly reductive group. Moreover, we study the…
The aim of this paper is to discuss a relationship between total positivity and planar directed networks. We show that the inverse boundary problem for these networks is naturally linked with the study of the totally nonnegative…
We study the positive theory of groups acting on trees and show that under the presence of weak small cancellation elements, the positive theory of the group is trivial, i.e. coincides with the positive theory of a non-abelian free group.…
This paper contains an exposition of the theory of character sheaves for reductive groups and some attempts to extend it to other cases: unipotent groups, reductive groups modulo the unipotent radical of a parabolic.
Addendum to the paper Combinatorics of the Modular Group II The Kontsevich integrals, hep-th/9201001, by C. Itzykson and J.-B. Zuber (3 pages)
This is the reply to a Comment by R. F. O'Connell (Phys. Rev. Lett. 87 (2001) 028901) on a paper written by the author (B. Vacchini, ``Completely positive quantum dissipation'', Phys.Rev.Lett. 84 (2000) 1374, arXiv:quant-ph/0002094).
As an extension of positive or almost positive diagrams and links, we introduce a notion of successively almost positive diagrams and links, and good successively almost positive diagrams and links. We review various properties of positive…
The new paper will be submitted.
We present a selection of results contributing to a structure theory of totally disconnected locally compact groups.
Enhancing the external validity of trial results is essential for their applicability to real-world populations. However, violations of the positivity assumption can limit both the generalizability and transportability of findings. To…
In "On the homotopy theory of arrangements," published in 1986, the authors gave a comprehensive survey of the subject. This article updates and continues the earlier article, noting some key open problems.
The paper studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. We illustrate the use of differential positivity on compact forward invariant sets for the characterization…
We give some statements that are equivalent to the existence of group inverses of Peirce corner matrices of a $2 \times 2$ block matrix and its generalized Schur complements. As applications, several new results for the Drazin inverses of…
We explain how a slight variant in the use of our recursive algorithm leads to improve the known lower bounds for the absolute trace of a totally positive algebraic integer. We also link the absolute trace of a totally positive algebraic…
The normalized totally positive bases are widely used in many fields.Based on the generalized Vandermonde determinant, the normalized total positivity of a kind of generalized toric-Bernstein basis is proved, which is defined on a set of…
In this note we give some new results concerning the subgroup commutativity degree of a finite group $G$. These are obtained by considering the minimum of subgroup commutativity degrees of all sections of $G$.
Let H be a reductive subgroup of a reductive group G over an algebraically closed field k. We consider the action of H on G^n, the n-fold Cartesian product of G with itself, by simultaneous conjugation. We give a purely algebraic…
We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…
We generalise our still-wide-open $q$-rious positivity conjecture from 2011 to a $q$-rious unimodality conjecture.