Erratum to: Tame Algebras Have Dense g-Vector Fans Plamondon, Pierre-Guy; Yurikusa, Toshiya; Keller, Bernhard
International mathematics research notices,
02/2024, Letnik:
2023, Številka:
4
Journal Article
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When this paper first published online, it contained a number of errors, which have nowbeen corrected online.The original paper did not clearly state that Pierre-Guy Plamondon and ToshiyaYurikusa ...were the author of the paper, but that Bernhard Keller was the author of theappendix.A dedication to the memory of Andrzej Skowronski was missing
Given a connected reductive algebraic group G over a finite field together with a representation of the dual group of G in GL(n), Braverman and Kazhdan defined an exotic Fourier operator on the space ...of complex valued functions on the finite group of rational points of G. In these notes we give an explicit formula for the Fourier kernel and a geometrical interpretation of this formula (as conjectured by Braverman and Kazhdan under some assumption).
A new construction of the associahedron was recently given by Arkani‐Hamed, Bai, He, and Yan in connection with the physics of scattering amplitudes. We show that their construction (suitably ...understood) can be applied to construct generalized associahedra of any simply laced Dynkin type. Unexpectedly, we also show that this same construction produces Newton polytopes for all the F$F$‐polynomials of the corresponding cluster algebras. In addition, we show that the toric variety associated to the g$g$‐vector fan has the property that its nef cone is simplicial.
We explore alternative functional or transport-entropy formulations of the Blaschke–Santaló inequality. In particular, we obtain new Blaschke–Santaló inequalities for s-concave functions. We also ...obtain new sharp symmetrized transport-entropy inequalities for a large class of spherically invariant probability measures, including the uniform measure on the unit Euclidean sphere and generalized Cauchy and Barenblatt distributions
This contribution considers the time‐fractional subdiffusion with a time‐dependent variable‐order fractional operator of order . It is assumed that is a piecewise constant function with a finite ...number of jumps. A proof technique based on the Fourier method and results from constant‐order fractional subdiffusion equations has been designed. This novel approach results in the well‐posedness of the problem.
Kazaniecki and Wojciechowskiproved in 2013 that every Fourier multiplier on $\dot{W}^{1,1}\left( \mathbb{R}^{d}\right) $ is a bounded continuous function on $\mathbb{R}^{d}$. This is a generalization ...of a previous result of Bonami and Poornima (1987)concerning homogeneous multipliers of degree zero. We further generalize the resultof Kazaniecki and Wojciechowski. We prove that, given an integer $l\geq1$,every multiplier on $\dot{W}^{l,1}\left( \mathbb{R}^{d}\right) $ or on $\dot{W}^{l,\infty}\left( \mathbb{R}^{d}\right) $ is a bounded continuous functionon $\mathbb{R}^{d}$. We obtain these results via a substantial simplification of the Riesz products technique used by Kazaniecki and Wojciechowski.
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