Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:Parkinson; James, Van Maldeghem, Hendrik Pages: 1517 - 1578 Abstract: To each automorphism of a spherical building, there is a naturally associated opposition diagram, which encodes the types of the simplices of the building that are mapped onto opposite simplices. If no chamber (that is, no maximal simplex) of the building is mapped onto an opposite chamber, then the automorphism is called domestic. In this paper, we give the complete classification of domestic automorphisms of split spherical buildings of types , , and . Moreover, for all split spherical buildings of exceptional type, we classify (i) the domestic homologies, (ii) the opposition diagrams arising from elements of the standard unipotent subgroup of the Chevalley group, and (iii) the automorphisms with opposition diagrams with at most two distinguished orbits encircled. Our results provide unexpected characterizations of long root elations and products of perpendicular long root elations in long root geometries, and analogues of the density theorem for connected linear algebraic groups in the setting of Chevalley groups over arbitrary fields. PubDate: 2021-07-05 DOI: 10.4153/S0008414X21000341

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Authors:Cibotaru; Daniel, Pereira, Wanderley Pages: 1579 - 1624 Abstract: Using a certain well-posed ODE problem introduced by Shilnikov in the sixties, Minervini proved the currential “fundamental Morse equation” of Harvey–Lawson but without the restrictive tameness condition for Morse gradient flows. Here, we construct local resolutions for the flow of a section of a fiber bundle endowed with a vertical vector field which is of Morse gradient type in every fiber in order to remove the tameness hypothesis from the currential homotopy formula proved by the first author. We apply this to produce currential deformations of odd degree closed forms naturally associated to any hermitian vector bundle endowed with a unitary endomorphism and metric compatible connection. A transgression formula involving smooth forms on a classifying space for odd K-theory is also given. PubDate: 2021-07-06 DOI: 10.4153/S0008414X21000353

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Authors:Agarwala; Susama, Fryer, Siân, Yeats, Karen Pages: 1625 - 1672 Abstract: Wilson loop diagrams are an important tool in studying scattering amplitudes of SYM theory and are known by previous work to be associated to positroids. In this paper, we study the structure of the associated positroids, as well as the structure of the denominator of the integrand defined by each diagram. We give an algorithm to derive the Grassmann necklace of the associated positroid directly from the Wilson loop diagram, and a recursive proof that the dimension of these cells is thrice the number of propagators in the diagram. We also show that the ideal generated by the denominator in the integrand is the radical of the ideal generated by the product of Grassmann necklace minors. PubDate: 2021-07-23 DOI: 10.4153/S0008414X21000377

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Authors:Ebrahimi-Fard; Kurusch, Patras, Frédéric, Tapia, Nikolas, Zambotti, Lorenzo Pages: 1673 - 1699 Abstract: Wick polynomials and Wick products are studied in the context of noncommutative probability theory. It is shown that free, Boolean, and conditionally free Wick polynomials can be defined and related through the action of the group of characters over a particular Hopf algebra. These results generalize our previous developments of a Hopf-algebraic approach to cumulants and Wick products in classical probability theory. PubDate: 2021-08-25 DOI: 10.4153/S0008414X21000407

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Authors:Randrianantoanina; Narcisse Pages: 1700 - 1744 Abstract: Let be a semifinite von Nemann algebra equipped with an increasing filtration of (semifinite) von Neumann subalgebras of . For , let denote the noncommutative column conditioned martingale Hardy space and denote the column “little” martingale BMO space associated with the filtration .We prove the following real interpolation identity: if and , then for , with equivalent quasi norms.For the case of complex interpolation, we obtain that if and , then for PubDate: 2021-08-25 DOI: 10.4153/S0008414X21000419

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Authors:Saksman; Eero, Soler i Gibert, Odí Pages: 1745 - 1770 Abstract: We determine the distance (up to a multiplicative constant) in the Zygmund class to the subspace The latter space is the image under the Bessel potential of the space , which is a nonhomogeneous version of the classical . Locally, consists of functions that together with their first derivatives are in . More generally, we consider the same question when the Zygmund class is replaced by the Hölder space with , and the corresponding subspace is , the image under of One should note here that Such results were known earlier only for PubDate: 2021-09-13 DOI: 10.4153/S0008414X21000523