6 research outputs found
On the hydrogen symmetry
We construct O(4)-invariant hydrogen wave function in coordinate representation
The Kazhdan-Lusztig conjecture for finite W-algebras
We study the representation theory of finite W-algebras. After introducing
parabolic subalgebras to describe the structure of W-algebras, we define the
Verma modules and give a conjecture for the Kac determinant. This allows us to
find the completely degenerate representations of the finite W-algebras. To
extract the irreducible representations we analyse the structure of singular
and subsingular vectors, and find that for W-algebras, in general the maximal
submodule of a Verma module is not generated by singular vectors only.
Surprisingly, the role of the (sub)singular vectors can be encapsulated in
terms of a `dual' analogue of the Kazhdan-Lusztig theorem for simple Lie
algebras. These involve dual relative Kazhdan-Lusztig polynomials. We support
our conjectures with some examples, and briefly discuss applications and the
generalisation to infinite W-algebras.Comment: 11 page
Energy and orientation of Bloch type domain walls in magnatics with mixed anisotropy
Theoretical energy calculation has been carried out for domain walls (DW) of several types with different gyration angles of the magnetization vector in ferrite-garnet crystals with mixed anisotropy (presence of the uniaxial EK and cubic anisotropy EK). The DW orientations satisfying to the energy minimum have been determined. It is shown that at parameter v = KU/K₁, the 1-st type DW (the magnetization vector in the neighboring domains have the same positive projection onto the axis [111], the normal to the film surface) are transformed into the 2-nd type DW (the projections of opposite signs, the angle between magnetization vectors being distinct from 180°)