Tensor Representations

1999 ◽  
pp. 2342-2353 ◽  
Author(s):  
Peter Herzig ◽  
Rainer Dirl
Keyword(s):  
Tensor Representations

scholarly journals H(4) tensor representations for the lattice Landau gauge gluon propagator and the estimation of lattice artefacts

2021 ◽  
Vol 103 (7) ◽  
Author(s):  
Guilherme T. R. Catumba ◽  
Orlando Oliveira ◽  
Paulo J. Silva
Keyword(s):  
Gluon Propagator ◽  
Landau Gauge ◽  
Tensor Representations

Macromodeling of I/O Buffers via Compressed Tensor Representations and Rational Approximations

2016 ◽  
Vol 6 (10) ◽  
pp. 1522-1534 ◽  
Author(s):  
Gianni Signorini ◽  
Claudio Siviero ◽  
Stefano Grivet-Talocia ◽  
Igor S. Stievano
Keyword(s):  
Rational Approximations ◽  
Tensor Representations

scholarly journals Thick branes in the scalar–tensor representation of f(R, T) gravity

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
João Luís Rosa ◽  
Matheus A. Marques ◽  
Dionisio Bazeia ◽  
Francisco S. N. Lobo
Keyword(s):  
Scalar Field ◽  
Matter Field ◽  
Energy Tensor ◽  
Tensor Representation ◽  
Observable Universe ◽  
Brane Model ◽  
Gravitational Fields ◽  
Stress Energy ◽  
Tensor Representations ◽  
The Stability

AbstractBraneworld scenarios consider our observable universe as a brane embedded in a five-dimensional bulk. In this work, we consider thick braneworld systems in the recently proposed dynamically equivalent scalar–tensor representation of f(R, T) gravity, where R is the Ricci scalar and T the trace of the stress–energy tensor. In the general $$f\left( R,T\right) $$ f R , T case we consider two different models: a brane model without matter fields where the geometry is supported solely by the gravitational fields, and a second model where matter is described by a scalar field with a potential. The particular cases for which the function $$f\left( R,T\right) $$ f R , T is separable in the forms $$F\left( R\right) +T$$ F R + T and $$R+G\left( T\right) $$ R + G T , which give rise to scalar–tensor representations with a single auxiliary scalar field, are studied separately. The stability of the gravitational sector is investigated and the models are shown to be stable against small perturbations of the metric. Furthermore, we show that in the $$f\left( R,T\right) $$ f R , T model in the presence of an extra matter field, the shape of the graviton zero-mode develops internal structure under appropriate choices of the parameters of the model.

Rational Tensor Representations of Hom(V, V) and an Extension of an Inequality of I. Schur.

1972 ◽  
Vol 24 (4) ◽  
pp. 686-695 ◽  
Author(s):  
Marvin Marcus ◽  
William Robert Gordon
Keyword(s):  
Tensor Product ◽  
Vector Space ◽  
Linear Operators ◽  
Inner Product ◽  
Complex Numbers ◽  
Dimensional Vector ◽  
Semi Group ◽  
Rational Representation ◽  
Dimensional Vector Space ◽  
Tensor Representations

Let V be an n-dimensional vector space over the complex numbers equipped with an inner product (x, y), and let (P, μ) be a symmetry class in the mth tensor product of V associated with a permutation group G and a character χ (see below). Then for each T ∊ Hom (V, V) the function φ which sends each m-tuple (v1, … , vm) of elements of V to the tensor μ(TV1, … , Tvm) is symmetric with respect to G and x, and so there is a unique linear map K(T) from P to P such that φ = K(T)μ.It is easily checked that K: Hom(V, V) → Hom(P, P) is a rational representation of the multiplicative semi-group in Hom(V, V): for any two linear operators S and T on VK(ST) = K(S)K(T).Moreover, if T is normal then, with respect to the inner product induced on P by the inner product on V (see below), K(T) is normal.

On the Dimension of an Irreducible Tensor Representation of the General Linear Group GL(d)

1970 ◽  
Vol 13 (3) ◽  
pp. 389-390
Author(s):  
J. A. J. Matthews ◽  
G. de B. Robinson
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
Irreducible Representations ◽  
Young Diagrams ◽  
Tensor Representation ◽  
Irreducible Tensor ◽  
Tensor Representations ◽  
Identity Representation ◽  
Raising Operator ◽  
Image Position

As has long been known, the irreducible tensor representations of GL(d) of rank n may be labeled by means of the irreducible representations of Sn, i.e., by means of the Young diagrams [λ], where λ1 + λ2 + … λr = n. We denote such a tensor representation by 〈λ〉. Using Young's raising operator Rij we can write [1, p. 42]1.1where the dot denotes the inducing process. For example, [3] . [2] is that representation of S5 induced by the identity representation of its subgroup S3 × S2.

scholarly journals THE SECOND FUNDAMENTAL THEOREM OF INVARIANT THEORY FOR THE ORTHOSYMPLECTIC SUPERGROUP

2019 ◽  
pp. 1-25 ◽  
Author(s):  
G. I. LEHRER ◽  
R. B. ZHANG
Keyword(s):  
Invariant Theory ◽  
Fundamental Theorem ◽  
Brauer Algebra ◽  
Tensor Space ◽  
General Linear Supergroup ◽  
Special Cases ◽  
Linear Description ◽  
Tensor Representations ◽  
Capelli Identities ◽  
Fundamental Theorems

The first fundamental theorem of invariant theory for the orthosymplectic supergroup scheme $\text{OSp}(m|2n)$ states that there is a full functor from the Brauer category with parameter $m-2n$ to the category of tensor representations of $\text{OSp}(m|2n)$ . This has recently been proved using algebraic supergeometry to relate the problem to the invariant theory of the general linear supergroup. In this work, we use the same circle of ideas to prove the second fundamental theorem for the orthosymplectic supergroup. Specifically, we give a linear description of the kernel of the surjective homomorphism from the Brauer algebra to endomorphisms of tensor space, which commute with the orthosymplectic supergroup. The main result has a clear and succinct formulation in terms of Brauer diagrams. Our proof includes, as special cases, new proofs of the corresponding second fundamental theorems for the classical orthogonal and symplectic groups, as well as their quantum analogues, which are independent of the Capelli identities. The results of this paper have led to the result that the map from the Brauer algebra ${\mathcal{B}}_{r}(m-2n)$ to endomorphisms of $V^{\otimes r}$ is an isomorphism if and only if $r<(m+1)(n+1)$ .

scholarly journals Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations

2020 ◽  
Vol 145 (3) ◽  
pp. 655-692
Author(s):  
Martin Eigel ◽  
Manuel Marschall ◽  
Max Pfeffer ◽  
Reinhold Schneider
Keyword(s):  
Tensor Representations ◽  
Stochastic Galerkin
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