501 research outputs found
Infinite tri-symmetric group, multiplication of double cosets, and checker topological field theories
We consider a product of three copies of infinite symmetric group and its
representations spherical with respect to the diagonal subgroup. We show that
such representations generate functors from a certain category of simplicial
two-dimensional surfaces to the category of Hilbert spaces and bounded linear
operators.Comment: 29 pages, 10 figure
Plancherel formula for Berezin deformation of on Riemannian symmetric space
Consider the space B of complex matrces with norm <1. There
exists a standard one-parameter family of unitary representations of the
pseudounitary group U(p,q) in the space of holomorphic functions on B (i.e.
scalar highest weight representations). Consider the restriction of
to the pseudoorthogonal group O(p,q).
The representation of O(p,q) in on the symmetric space
is a limit of the representations in some
precise sence. Spectrum of a representation is comlicated and it depends
on .
We obtain the complete Plancherel formula for the representations for
all admissible values of the parameter . We also extend this result to
all classical noncompact and compact Riemannian symmetric spaces
On action of the Virasoro algebra on the space of univalent functions
We obtain explicit expressions for differential operators defining the action
of the Virasoro algebra on the space of univalent functions. We also obtain an
explicit Taylor decomposition for Schwarzian derivative and a formula for the
Grunsky coefficients.Comment: 15
On compression of Bruhat-Tits buildings
We obtain an analog of the compression of angles theorem in symmetric spaces
for Bruhat--Tits buildings of the type .
More precisely, consider a -adic linear space and the set of
all lattices in . The complex distance in is a complete system of
invariants of a pair of points of under the action of the complete
linear group. An element of a Nazarov semigroup is a lattice in the duplicated
linear space . We investigate behavior of the complex distance under
the action of the Nazarov semigroup on the set .Comment: 6 page
Groups of hierarchomorphisms of trees and related Hilbert spaces
Consider an infinite tree. A hierarchomorphism (spheromorphism) is a
homeomorphism of the absolute which can be extended to the tree except a finite
subtree. Examples of groups of hierarchomorphisms: groups of locally analitic
diffeomorphisms of -adic line; also Richard Thompson groups. The groups of
hierarchomorphisms have some properties similar to the group of diffeomorphisms
of the circle. We discuss actions of groups of ierarchomorphisms in some
natural Hilbert spaces associated with trees.Comment: 22 pages, two picture
Difference Sturm--Liouville problems in the imaginary direction
We consider difference operators in on of the form where is the imaginary unit. The
domain of definiteness are functions holomorphic in a strip with some
conditions of decreasing at infinity. Problems of such type with discrete
spectra are well known (Meixner--Pollaszek, continuous Hahn, continuous dual
Hahn, and Wilson hypergeometric orthogonal polynomials).
We write explicit spectral decompositions for several operators with
continuous spectra. We also discuss analogs of 'boundary conditions' for such
operators.Comment: 27p
- …