We find a connection between the character ofVnλ and the respective weight polytopes.
First we show that the representation ofG×G on eachG-biinvariant irreducible reproducing kernel Hilbert space in Hol(D) is a highest weight representation whose kernel is the character of a highest weight representation ofG.
For a classical semisimple Lie algebra, we construct equivariant line bundles whose global sections afford representations with a nilpotentp-character.
Under the obvious restriction map, the space of biinvariants is proved isomorphic to the Weyl group invariants of the character group ring associated to the restricted roots.
Finite complex reflection groups have the remarkable property that the character field k of their reflection representation is a splitting field, that is, every irreducible complex representation can be realized over k.
Soergel who has computed the characters of tilting modules.
Fork=1, we give explicit formulas for the characters.
We also present recursion relations satisfied by the characters and the monomial bases.
The canonical and dual canonical basis of the Fock space are computed and then used to derive the finite-dimensional tilting and irreducible characters for the Lie superalgebra osp(2|2n).
When one expands a Schur function in terms of the irreducible characters of the symplectic (or orthogonal) group, the coefficient of the trivial character is 0 unless the indexing partition has an appropriate form.
A space [Figure not available: see fulltext.] is constructed and some characterizations of space [Figure not available: see fulltext.] are given.
It is shown that the classical Fourier transform is extended to the distribution space [Figure not available: see fulltext.], which can be embedded into the Schwartz distribution space [Figure not available: see fulltext.] continuously.
This figure was generally consistent with that estimated by Shannon index, i.e., the genetic differentiation among populations was relatively high, but that within populations was relatively low.
Computer simulation shows that our model can figure out the breakage of the coexistence of majority and minority after a period's evolution.
The relative contents of AOS in cells predicted by the ANN model agreed well with the experimental data and three notable stages of AOS increase were observed from the 3D figure of AOS generation.
The heating effects in different regions with different heating conditions have been presented in figures.
Fractal theory, used to study natural figures and images with self-similarity but without characteristic lengths, offers an effective tool to investigate quantitatively the complex systems such as soil.
In this paper, ten examples are given with figures.
There was a positive correlation between the ADM expression and mitotic figures in LES (P >amp;lt; 0.05): the more mitotic figures, the higher levels of the ADM expression and poor prognosis.
The necessary pole figures data can be collected holistically by the X-ray area detectors, after which the volume fraction of the texture components in Gaussian forms is obtained.