We classify simple Whittaker modules for classical Lie superalgebras in terms of their parabolic decompositions. establish a type Miličić–Soergel equivalence category and Harish–Chandra bimodules. For I, we reduce the problem composition factors standard to that Verma BGG categories $${\mathcal {O}}$$ . As consequence, series over general linear $$\mathfrak {gl}(m|n)$$ ortho-symplectic {osp}(2|...

Parabolic subalgebras of semi-simple Lie algebras decompose as p = m⊕ n where m is a Levi factor and n the corresponding nilradical. By Richardsons theorem [R], there exists an open orbit under the action of the adjoint group P on the nilradical. The elements of this dense orbits are known as Richardson elements. In this paper we describe a normal form for Richardson elements in the classical c...

Lie bialgebra structures on e(2) are classified. For two Lie bialgebra structures which are not coboundaries (i.e. which are not determined by a classical r-matrix) we solve the cocycle condition, find the Lie-Poisson brackets and obtain quantum group relations. There is one to one correspondence between Lie bialgebra structures on e(2) and possible quantum deformations of U (e(2)) and E(2).

It is well known that the category of super Lie groups (SLG) is equivalent to the category of super Harish-Chandra pairs (SHCP). Using this equivalence, we define the category of unitary representations (UR's) of a super Lie group. We give an extension of the classical inducing construction and Mackey imprimitivity theorem to this setting. We use our results to classify the irreducible unitary ...

We consider the classical problem of construction invariant tori exploiting suitable Hamiltonian normal forms. This kind approach can be translated by means Lie series method into explicit computational algorithms, which are particularly for applications in field Celestial Mechanics. First, algorithm constructing Kolmogorov form is described detail. Then, extension to lower-dimensional elliptic...