Sentence examples for weight representations from inspiring English sources

In particular we construct the L2-realization of all unitary highest weight representations, including the vector-valued case.

The Fock model realization of unitary highest weight representations of U p, q) is the fundamental tool used to implement this construction.

Finally we show that the operator-valued measures corresponding to the vector valued highest weight representations have densities of a rather weak type with respect to Wishart distributions which makes it possible to determine their "supports".

In this paper we study spherical unitary highest weight representations associated to a compactly causal symmetric space and use the results to prove estimates for the corresponding spherical functions of the c-dual non-compactly causal symmetric space.

For unitary highest weight representations we obtain a characterization of those highest weights for which the closure of the image of this map is convex, i.e., equal to the convex hull of the highest weight orbit.

We give a classification of the algebraic category of unitary highest weight modules for such Lie algebras and show that infinite dimensional versions of the Lie algebras so 2, n) have no unitary highest weight representations and thus do not meet the physical requirement of having positive energy.

To certain highest weights λ, we associate a first-order group invariant linear differential operator Dλ; whose kernel contains a unitary highest weight representation with highest weight λ.

Notably, this class of ligands has been extensively utilized by Mascharak and co-workers to provide low-molecular-weight representations of metallo-proteins/enzymes such as bleomycins, nitrile hydratase.

Figure 11 Neurons weights representation after STDP training.

Now, Howe duality (Proposition 2.2) implies that (mathfrak {a}(V)^K) is the representation space for an irreducible highest-weight representation (rho _*) of the Howe dual partner (mathfrak {g}) of K in the orthosymplectic Lie superalgebra (mathfrak {osp}(W)).

These words were then subsequently clustered on the basis of sequence similarity, and positional weight matrix representations were generated from the clusters.