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The celebrated Paley-Wiener theorem naturally identifies the spaces of bandlimited functions with subspaces of entire functions of exponential type. Recently, it has been shown that these spaces remain invariant only under composition with…

Complex Variables · Mathematics 2012-10-10 S. Mukherjee , F. Jafari , J. E. McInroy

Let $G$ be a complex reductive group, $T$ be a maximal torus of $G$, $B$ be a Borel subgroup of $G$ containing $T$, $W$ be the Weyl group of $G$ with respect to $T$. To each element $w$ of $W$ one can associate the Schubert subvariety $X_w$…

Algebraic Geometry · Mathematics 2015-01-13 Mikhail A. Bochkarev , Mikhail V. Ignatyev , Aleksandr A. Shevchenko

We define Cayley structures as a field of Cayley's ruled cubic surfaces over a four dimensional manifold and motivate their study by showing their similarity to indefinite conformal structures and their link to differential equations. In…

Differential Geometry · Mathematics 2020-10-05 Wojciech Kryński , Omid Makhmali

We associate a quotient of superspace to any hyperplane arrangement by considering the differential closure of an ideal generated by powers of certain homogeneous linear forms. This quotient is a superspace analogue of the external…

Combinatorics · Mathematics 2024-04-03 Brendon Rhoades , Vasu Tewari , Andy Wilson

Given a Baumslag-Solitar group, we study its space of subgroups from a topological and dynamical perspective. We first determine its perfect kernel (the largest closed subset without isolated points). We then bring to light a natural…

Group Theory · Mathematics 2024-11-11 Alessandro Carderi , Damien Gaboriau , François Le Maître , Yves Stalder

A celebrated theorem of Pimsner states that a covariant representation $T$ of a $C^*$-correspondence $E$ extends to a $C^*$-representation of the Toeplitz algebra of $E$ if and only if $T$ is isometric. This paper is mainly concerned with…

Operator Algebras · Mathematics 2011-03-31 Ami Viselter

Let G/H be a unimodular real spherical space which is either absolutely spherical or wave-front. It is shown that every tempered representation of G/H embeds into a relative discrete series of a boundary degeneration of G/H. If in addition…

Representation Theory · Mathematics 2022-09-23 Friedrich Knop , Bernhard Krötz , Henrik Schlichtkrull

We consider tangent cones of Schubert varieties in the complete flag variety, and investigate the problem when the tangent cones of two different Schubert varieties coincide. We give a sufficient condition for such coincidence, and…

Representation Theory · Mathematics 2017-06-12 Dmitry Fuchs , Alexandre Kirillov , Sophie Morier-Genoud , Valentin Ovsienko

When considered as submanifolds of Euclidean space, the Riemannian geometry of the round sphere and the Clifford torus may be formulated in terms of Poisson algebraic expressions involving the embedding coordinates, and a central object is…

Quantum Algebra · Mathematics 2015-06-16 Joakim Arnlind

A subvariety of a quasi-projective complex variety $X$ is called ``universally irreducible'' if its preimage inside the universal cover of $X$ is irreducible. In this paper we investigate sufficient conditions for universal irreducibility.…

Algebraic Geometry · Mathematics 2023-12-12 Gabriele Mondello , Riccardo Salvati Manni

We construct a compact metric space that has any other compact metric space as a tangent, with respect to the Gromov-Hausdorff distance, at all points. Furthermore, we give examples of compact sets in the Euclidean unit cube, that have…

Metric Geometry · Mathematics 2020-10-02 Changhao Chen , Eino Rossi

The paper contains a characterization of compact groups $G\subseteq\GL(V)$, where $V$ is a finite dimensional real vector space, which have the following property \SP{}: the family of convex hulls of $G$-orbits is a semigroup with respect…

Metric Geometry · Mathematics 2010-09-23 V. Gichev

We prove a reduced version of the Chevalley restriction conjecture on the commuting scheme posed by T.H. Chen and B.C. Ng\^o, extending the results of Hunziker for classical groups. In particular, we prove that for any connected reductive…

Representation Theory · Mathematics 2025-05-01 Josh Katz

This paper consists of two main results. In the first one we describe all Kaehler immersions of a bounded symmetric domain into the infinite dimensional complex projective space in terms of the Wallach set of the domain. In the second one…

Differential Geometry · Mathematics 2012-04-16 Andrea Loi , Michela Zedda

We examine how the square-integrable function subspaces are transformed using the holomorphic Fourier transform. On account of this, the extended Paley-Wiener theorem over the Hardy-Sobolev spaces is produced. The theorem also asserts that…

Functional Analysis · Mathematics 2024-03-19 Detian Liu , Haichou Li , Kit Ian Kou

Given a hypersurface in a complex projective space, we prove that the multidegrees of its toric polar map agree, up to sign, with the coefficients of the Chern-Schwartz-MacPherson class of a distinguished open set, namely the complement of…

Algebraic Geometry · Mathematics 2023-05-03 Thiago Fassarella , Nivaldo Medeiros , Rodrigo Salomão

We study polar orbitopes, i.e. convex hulls of orbits of a polar representation of a compact Lie group. The face structure is studied by means of the gradient momentum map and it is shown that every face is exposed and is again a polar…

Representation Theory · Mathematics 2013-04-24 Leonardo Biliotti , Alessandro Ghigi , Peter Heinzner

We find the complete rational homology for the finite subset spaces of a $d$-dimensional sphere. We also determine the integral homology in top $d$ degrees and obtain a partial description of it in codimension $d$.

Algebraic Topology · Mathematics 2026-03-03 Jacob Mostovoy

This article provides a general framework in the context of category theory where one can recognize as particular instances of the same abstract construction several notions of completion, envelope, and hull, such as the Boolean algebra…

Category Theory · Mathematics 2026-03-17 Ivan Di Liberti , Martino Lupini

We represent a bilinear Calder\'on-Zygmund operator at a given smoothness level as a finite sum of cancellative, complexity zero operators, involving smooth wavelet forms, and continuous paraproduct forms. This representation results in a…

Classical Analysis and ODEs · Mathematics 2023-04-26 Francesco Di Plinio , A. Walton Green , Brett D. Wick