Non-Vanishing and Orthogonal Basis of Symmetry Classes of Tensors
نویسندگان
چکیده
By Cayley’s theorem, any finite group G of order n can be regarded as a subgroup of the symmetric group $n. Let χ be any irreducible complex character of G and let V n χ (G) denote the symmetry classes of tensors associated with G and χ. In this paper assuming the Cayley representation of G, we obtain a formula for the dimension of V n χ (G) and discuss its non-vanishing in general. A necessary condition for the existence of the orthogonal basis of decomposable symmetrized tensors for V n χ (G) is also obtained.
منابع مشابه
Monomial Irreducible sln-Modules
In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.
متن کاملA Note on the Orthogonal Basis of a Certain Full Symmetry Class of Tensors
It is shown that the full symmetry class of tensors associated with the irreducible character [2, 1n−2] of Sn does not have an orthogonal basis consisting of decomposable symmetrized tensors.
متن کاملAn Ab initio and chemical shielding tensors calculations for Nucleotide 5’-Monophosphates in the Gas phase
Structural and magnetic properties of purine and pyrimidine nucleotides (CMP, UMP, dTMP, AMP, GMP, IMP) were studied at different levels of ab initio molecular orbital theory. These calculations were performed at the hartree-fock level and density functional B3LYP methods. Geometries were fully optimized by following Cs symmetry restrictions. The standard 6-31G** basis set which includes polari...
متن کاملSome new families of definite polynomials and the composition conjectures
The planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjectur...
متن کاملOn the decomposable numerical range of operators
Let $V$ be an $n$-dimensional complex inner product space. Suppose $H$ is a subgroup of the symmetric group of degree $m$, and $chi :Hrightarrow mathbb{C} $ is an irreducible character (not necessarily linear). Denote by $V_{chi}(H)$ the symmetry class of tensors associated with $H$ and $chi$. Let $K(T)in (V_{chi}(H))$ be the operator induced by $Tin text{End}(V)$. Th...
متن کامل