99 research outputs found
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
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
On the Ado Theorem for finite Lie conformal algebras with Levi decomposition
We prove that a finite torsion-free conformal Lie algebra with a splitting
solvable radical has a finite faithful conformal representation.Comment: 11 page
Notes on Stein-Sahi representations and some problems of non harmonic analysis
We discuss one natural class of kernels on pseudo-Riemannian symmetric
spaces.Comment: 40p
Infinite-dimensional -adic groups, semigroups of double cosets, and inner functions on Bruhat--Tits builldings
We construct -adic analogs of operator colligations and their
characteristic functions. Consider a -adic group , its subgroup , and the subgroup
embedded to diagonally. We show that double cosets
admit a structure of a semigroup, acts naturally in -fixed vectors
of unitary representations of . For each double coset we assign a
'characteristic function', which sends a certain Bruhat--Tits building to
another building (buildings are finite-dimensional); image of the distinguished
boundary is contained in the distinguished boundary. The latter building admits
a structure of (Nazarov) semigroup, the product in corresponds to a
point-wise product of characteristic functions.Comment: new version of the paper, 47pp, 3 figure
- …