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G L n -Invariant tensors and graphs

Martin Markl (2008)

Archivum Mathematicum

We describe a correspondence between GL n -invariant tensors and graphs. We then show how this correspondence accommodates various types of symmetries and orientations.

Gap universality of generalized Wigner and β -ensembles

László Erdős, Horng-Tzer Yau (2015)

Journal of the European Mathematical Society

We consider generalized Wigner ensembles and general β -ensembles with analytic potentials for any β 1 . The recent universality results in particular assert that the local averages of consecutive eigenvalue gaps in the bulk of the spectrum are universal in the sense that they coincide with those of the corresponding Gaussian β -ensembles. In this article, we show that local averaging is not necessary for this result, i.e. we prove that the single gap distributions in the bulk are universal. In fact,...

General construction of Banach-Grassmann algebras

Vladimir G. Pestov (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We show that a free graded commutative Banach algebra over a (purely odd) Banach space E is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if E is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.

General theory of Lie derivatives for Lorentz tensors

Lorenzo Fatibene, Mauro Francaviglia (2011)

Communications in Mathematics

We show how the ad hoc prescriptions appearing in 2001 for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier, in a much more general setting encompassing older results of Y. Kosmann about Lie derivatives of spinors.

Generalizations of Milne’s U ( n + 1 ) q -Chu-Vandermonde summation

Jian-Ping Fang (2016)

Czechoslovak Mathematical Journal

We derive two identities for multiple basic hyper-geometric series associated with the unitary U ( n + 1 ) group. In order to get the two identities, we first present two known q -exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two U ( n + 1 ) q -Chu-Vandermonde summations established by Milne, we arrive at our...

Generalizations of Nekrasov matrices and applications

Ljiljana Cvetković, Vladimir Kostić, Maja Nedović (2015)

Open Mathematics

In this paper we present a nonsingularity result which is a generalization of Nekrasov property by using two different permutations of the index set. The main motivation comes from the following observation: matrices that are Nekrasov matrices up to the same permutations of rows and columns, are nonsingular. But, testing all the permutations of the index set for the given matrix is too expensive. So, in some cases, our new nonsingularity criterion allows us to use the results already calculated...

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