34 research outputs found
The Radon transform and its dual for limits of symmetric spaces
The Radon transform and its dual are central objects in geometric analysis on
Riemannian symmetric spaces of the noncompact type. In this article we study
algebraic versions of those transforms on inductive limits of symmetric spaces.
In particular, we show that normalized versions exists on some spaces of
regular functions on the limit. We give a formula for the normalized transform
using integral kernels and relate them to limits of double fibration transforms
on spheres
Noncommutative symmetric functions and Laplace operators for classical Lie algebras
New systems of Laplace (Casimir) operators for the orthogonal and symplectic
Lie algebras are constructed. The operators are expressed in terms of paths in
graphs related to matrices formed by the generators of these Lie algebras with
the use of some properties of the noncommutative symmetric functions associated
with a matrix. The decomposition of the Sklyanin determinant into a product of
quasi-determinants play the main role in the construction. Analogous
decomposition for the quantum determinant provides an alternative proof of the
known construction for the Lie algebra gl(N).Comment: 25 page
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
Integrability and Fusion Algebra for Quantum Mappings
We apply the fusion procedure to a quantum Yang-Baxter algebra associated
with time-discrete integrable systems, notably integrable quantum mappings. We
present a general construction of higher-order quantum invariants for these
systems. As an important class of examples, we present the Yang-Baxter
structure of the Gel'fand-Dikii mapping hierarchy, that we have introduced in
previous papers, together with the corresponding explicit commuting family of
quantum invariants.Comment: 26 page
C*-simplicity and the unique trace property for discrete groups
In this paper, we introduce new methods for working with group and crossed product C*-algebras that allow us to settle the longstanding open problem of characterizing groups with the unique trace property