Irreducible representations for generating (3+d)-dimensional modulated structures

Finite-dimensional Irreducible Representations of Twisted Yangians

We study quantized enveloping algebras called twisted Yangians. They are analogues of the Yangian Y(gl(N)) for the classical Lie algebras of B, C, and D series. The twisted Yangians are subalgebras in Y(gl(N)) and coideals with respect to the coproduct in Y(gl(N)). We give a complete description of their finite-dimensional irreducible representations. Every such representation is highest weight...

GENERIC IRREDUCIBLE REPRESENTATIONS OFFINITE - DIMENSIONAL LIE SUPERALGEBRASIvan

A theory of highest weight modules over an arbitrary nite-dimensional Lie su-peralgebra is constructed. A necessary and suucient condition for the nite-dimensionality of such modules is proved. Generic nite-dimensional irreducible representations are deened and an explicit character formula for such representations is written down. It is conjectured that this formula applies to any generic nite...

Using Irreducible Group Representations for Invariant 3D Shape Description

Invariant feature representations for 3D objects are one of the basic needs in 3D object retrieval and classification. One tool to obtain rotation invariance are Spherical Harmonics, which are an orthogonal basis for the functions defined on the 2-sphere. We show that the irreducible representations of the 3D rotation group, which acts on the Spherical Harmonic representation, can give more inf...

Irreducible Representations of Infinite-dimensional Transformation Groups and Lie Algebras

Irreducible representations of metrizable spaces and strongly countable-dimensional spaces

We generalize Freudenthal’s theory of irreducible representations of metrizable compacta by inverse sequences of compact polyhedra to the class of all metrizable spaces. Our representations consist of inverse sequences of completely metrizable polyhedra which are ANR’s. They are extendable: any such representation of a closed subspace of a given metrizable space extends to another such of the e...