63 citations · 149 across the 18 of their papers we have counts for
11 papers · 1 filter
On infinite-dimensional limit of the Steinberg representations
Yury A. Neretin
We present a construction of the Steinberg representation admitting an automatic pass to an infinite-dimensional limit.
Double cosets for $\SU(2)\times...\times\SU(2)$ and outer automorphisms of free groups
Yuri A. Neretin
Consider the space of double cosets of the product of copies of $\SU(2)$ with respect to the diagonal subgroup. We get a parametrization of this space, the radial part of the H…
Stein--Sahi complementary series and their degenerations
Yuri A. Neretin
The aim of the paper is an introduction to Stein--Sahi complementary series, holomorphic series, and 'unipotent representations'. We also discuss some open problems related to thes…
Notes on Sobolev spaces on compact classical groups and Stein--Sahi representations
Yuri A. Neretin
We discuss kernels on complact classical groups $G=\U(n)$, $\OO(2n)$, $\Sp(n)$ defined by the formula . We obtain the explicit Plancherel formula for these…
On compression of Bruhat-Tits buildings
Yuri A. Neretin
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 th…
Beta-function of Bruhat--Tits buildings and deformation of on the space of lattices
Yurii A. Neretin
For the space of all the lattices in a -adic -dimensional linear space we obtain an analog of matrix beta-functions; this beta-function has a degeneration to the Tama…
A construction of finite-dimensional faithful representation of Lie algebra
Yurii A. Neretin
We give a natural proof of the Ado theorem.
Action of overalgebra in Plancherel decomposition and shift operators in imaginary direction
Yurii A. Neretin
Consider the Plancherel decomposition of the tensor product of a highest weight and a lowest weight unitary representations of . We construct explicitly the action of the Lie…
Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary
Yurii A. Neretin
Consider a finite dimensional (generally reducible) polynomial representation ρof GL_n. A projective compactification of GL_n is the closure of ρ(GL_n) in the space of all operator…
Separation of spectra in analysis of Berezin kernels
Yu. A. Neretin
Consider an unitary highest weight representation of a group U(p,q) in holomorphic functions on the symmetric space U(p,q)/U(p)\times U(q). Consider its restriction ρto the subgrou…
Matrix analogs of B-functions and Plancherel formula for Berezin kernel representations
Yu. A. Neretin
We obtain a family of matrix integrals which decompose to a product of Gamma-functions (they have some relations with S.G.Gindikin 'Beta', but generally speaking essentially differ…