Article
Mathematics
Sanghoon Baek, Yeongjong Kim
Summary: This study determines the essential dimension of an arbitrary semisimple group of type B, denoted as G, over a field of characteristic 0. The group G can be represented as (Spin(2n1 + 1) x ... x Spin(2nm + 1))/& mu;, where n1, ... , nm & GE; 7, and & mu; is a central subgroup of Spin(2n1 + 1) x ... x Spin(2nm + 1) that does not contain the center of Spin(2ni + 1) as a direct factor for every i = 1, ... , m.
JOURNAL OF ALGEBRA
(2023)
Article
Mathematics
Zinovy Reichstein, Federico Scavia
Summary: This paper investigates the essential dimension of algebraic groups over a p-closed field at the prime p, and compares it with previous research. In a specific case, we prove a conjecture related to the essential dimension.
ALGEBRAIC GEOMETRY
(2021)
Article
Mathematics, Applied
Pieter Kleer, Hans Simon
Summary: We provide tight bounds on the relation between the primal and dual of various combinatorial dimensions for multi-valued function classes. These dimensions are important in the field of learning theory. We review classical results that bound the dual dimension of a function class based on its primal, and introduce almost matching lower bounds. Furthermore, we generalize Assouad's well-known bound on primal and dual VC-dimensions of binary function classes to multi-valued function classes.
DISCRETE APPLIED MATHEMATICS
(2023)
Article
Mathematics
Joshua P. Swanson, Nolan R. Wallach
Summary: The paper presents a type-independent construction for explicit basis of semi-invariant harmonic differential forms of pseudo-reflection groups in characteristic zero. It completely describes the structure of chi-isotypic components of corresponding super coinvariant algebras, and verifies a specialization of a conjecture, providing a representation-theoretic model for the Delta conjecture. The top-down approach using Cartan's exterior calculus is dual to related work describing invariant differential forms.
JOURNAL OF COMBINATORIAL THEORY SERIES A
(2021)
Article
Optics
Chunming Jiang, Dong Yao, Lingtong Meng, Chunhui Yan, Honghai Shen
Summary: Polarization remote sensing technology modifies the polarization information of the target through modulation by the optical system. Adding a lens group combined with mirrors effectively suppresses polarization aberrations, resulting in reduced diattenuation and retardance values, as well as corrected polarization cross-coupled energy.
Article
Mathematics, Applied
Rostislav A. Devyatov, Nikita A. Karpenko, Alexander S. Merkurjev
Summary: This study establishes the sharp upper bounds on the indexes for most of the twisted flag varieties under the spin groups Spin(n).
FORUM OF MATHEMATICS SIGMA
(2021)
Article
Mathematics
Michael Kapovich, Alex Kontorovich
Summary: We introduce the concept of Kleinian Sphere Packing, a generalization of crystallographic (Apollonian-like) sphere packings. Unlike crystallographic packings, Kleinian packings exist in all dimensions, and so do superintegral ones. We extend the Arithmeticity Theorem to Kleinian packings, showing that the superintegral ones come from Q-arithmetic lattices of simplest type. Similarly, this applies to more general objects called Kleinian Bugs, where spheres may meet at finitely many dihedral angles p/m without being disjoint. We address two questions from Kontorovich and Nakamura (2019): (i) the general falseness of the Arithmeticity Theorem over number fields, and (ii) the fact that integral packings only arise from non-uniform lattices.
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
(2023)
Article
Mathematics
Jialun Li, Frederic Naud, Wenyu Pan
Summary: This paper examines the properties of Zariski-dense Kleinian Schottky subgroups of PSL2(C), showing polynomial decay of the Fourier transform in the limit and concluding positive Fourier dimension for all limit sets. The results are an extension of Bourgain and Dyatlov's findings in PSL2(R) and rely on the decay of exponential sums based on sum-product estimates on C. The bounds on exponential sums are based on a delicate nonconcentration hypothesis proven using representation theory and regularity estimates for stationary measures of random walks on linear groups.
DUKE MATHEMATICAL JOURNAL
(2021)
Article
Mathematics
Yi Wang, Jingbo Xia
Summary: This paper examines a bounded strongly pseudo-convex domain and the Toeplitz algebra on the Bergman space. It shows certain properties on specific Omegas and uses new ideas and techniques to derive general conclusions. The findings highlight the essential commutants of operators in different settings, as well as the compactness of certain operators under specific conditions.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Mathematics
Hannah Knight
Summary: In this paper, the essential p-dimension of the split finite quasi-simple groups of classical Lie type at the defining prime, including general linear and special linear groups, symplectic groups, and orthogonal groups, is computed. (c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
JOURNAL OF ALGEBRA
(2023)
Article
Physics, Mathematical
Yang Qiu, Zhenghan Wang
Summary: In this paper, representations of motion groups of links in S3 with generalized axes are computed using Dijkgraaf-Witten TQFTs inspired by dimension reduction. The results represent a step towards a twisted generalization of DW theories, as stated in Conjecture 1.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2021)
Article
Mathematics, Applied
Ke Ou
Summary: In this paper, the modular invariants for certain pseudo-reflection subgroups of the finite general linear group GLn(q) acting on the tensor product of the symmetric algebra S center dot(V) and the exterior algebra perpendicular to center dot(V) of the natural GLn(q)-module V are determined. The focus is on the case when the pseudo-reflection groups are subgroups of the parabolic subgroup of GLn(q) which are generalizations of Weyl groups of Cartan type Lie algebra.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2023)
Article
Mathematics
Lewis Bowen, Peter Burton
Summary: This article introduces the concept of soficity for locally compact groups and lists several open problems.
ISRAEL JOURNAL OF MATHEMATICS
(2022)
Article
Physics, Multidisciplinary
Hai Li, Xiang Hu, Gang Ouyang
Summary: In this study, we theoretically investigate the transport properties in normal-superconducting junctions based on semi-Dirac materials (SDMs) using the framework of Bogoliubov-de Gennes equation. Due to the intrinsic anisotropy of SDMs, the configuration of Andreev reflection (AR) and the differential conductance strongly depend on the orientation. The results show that for transport along the linear dispersion direction, there is a clear crossover from retro AR to specular AR with increasing bias-voltage, and the differential conductance oscillates without decaying with the interfacial barrier strength. Conversely, for transport along the quadratic dispersion direction, the boundary between retro AR and specular AR becomes ambiguous as the orientation angle increases, and the differential conductance decays with increasing momentum mismatch or interfacial barrier strength. The pseudo-spin textures are used to illustrate the underlying physics behind the anisotropic coherent transport properties.
NEW JOURNAL OF PHYSICS
(2022)
Review
Mathematics, Applied
Fuhai Zhu, Zhiqi Chen, Ke Liang
Summary: This paper discusses the properties of the isometry group of a simple Lie group G with a left-invariant pseudo-Riemannan metric, proving that the isometry group is compact. It also states that the identity component of the isometry group is compact when G is not simply-connected.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
Mathematics
Alexander Duncan
TRANSFORMATION GROUPS
(2016)
Article
Mathematics
Igor Dolgachev, Alexander Duncan
ALGEBRA & NUMBER THEORY
(2018)
Article
Mathematics
Alexander Duncan
COMMENTARII MATHEMATICI HELVETICI
(2013)
Article
Mathematics
I Dolgachev, A. Duncan
IZVESTIYA MATHEMATICS
(2019)
Article
Mathematics
Matthew R. Ballard, Alexander Duncan, Patrick K. McFaddin
Summary: The full exceptional collections of vector bundles on centrally symmetric smooth, Fano arithmetic toric varieties are studied.
MATHEMATISCHE NACHRICHTEN
(2022)
Article
Mathematics
Matthew R. Ballard, Alexander Duncan, Patrick K. McFaddin
EUROPEAN JOURNAL OF MATHEMATICS
(2019)
Article
Mathematics
Matthew Ballard, Alexander Duncan, Patrick McFaddin
ANNALS OF K-THEORY
(2019)
Article
Mathematics
Alexander Duncan
EUROPEAN JOURNAL OF MATHEMATICS
(2016)
Article
Mathematics
Igor Dolgachev, Alexander Duncan
ALGEBRAIC GEOMETRY
(2016)
Article
Mathematics
Alexander Duncan, Zinovy Reichstein
JOURNAL OF ALGEBRAIC GEOMETRY
(2015)
Article
Mathematics
Alexander Duncan
MATHEMATICAL RESEARCH LETTERS
(2010)
Article
Mathematics, Applied
Alexander Duncan, Zinovy Reichstein
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2009)
