63 citations · 149 across the 18 of their papers we have counts for
21 papers
On algebras of double cosets of symmetric groups with respect to Young subgroups
Yury A. Neretin
We consider the subalgebra in the group algebra of the symmetric group consisting of all functions invariant with respect to left and right shifts by elem…
Diffeomorphisms groups of tame Cantor sets and Thompson-like groups
Louis Funar, Yurii Neretin
The group of -diffeomorphisms of any sparse Cantor subset of a manifold is countable and discrete (possibly trivial). Thompson's groups come out of this construction…
Biinvariant functions on the group of transformations leaving a measure quasiinvariant
Yuri A. Neretin
Let be the group of transformations of a Lebesgue space leaving the measure quasiinvariant, let be its subgroup consisting of transformations preserving the measure. We…
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.
Felix Alexandrovich Berezin and his work
Alexander Karabegov, Yuri Neretin, Theodore Voronov
This is a survey of Berezin's work focused on three topics: representation theory, general concept of quantization, and supermathematics.
Rolling of Coxeter polyhedra along mirrors
Dmitri V. Alekseevsky, Peter W. Michor, Yurii A. Neretin
The topic of the paper are developments of -dimensional Coxeter polyhedra. We show that the surface of such polyhedron admits a canonical cutting such that each piece can be cov…
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…
Structures of boson and fermion Fock spaces in the space of symmetric functions
Yurii A. Neretin
We realize the Weil representation of infinite dimensional symplectic group and spinor representation of infinite-dimensional group by linear operators in the space of symmetr…
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…
Hua type integrals over unitary groups and over projective limits of unitary groups
Yurii A. Neretin
We discuss some natural maps from a unitary group U(n) to a smaller group U(n-m) (these maps are versions of the Livshic characteristic function). We calculate explicitly the direc…
On Jordan angles and triangle inequality in Grassmannian
Yurii A. Neretin
We obtain the following version of Lidskii theorem. Let L, M, N be p-dimensional subspaces in R^n. Let ψ_j be the angles between L and M, let ϕ_j be the angles between M and N, and…
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…
A remark on boson-fermion correspondence
Yu. A. Neretin
We give a simple explanaition of classical boson-fermion correspondence.
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…
Hinges and geometric constructions of boundaries of symmetric spaces
Yurii A. Neretin
We give elementary constructions for Satake-Furstenberg, Martin and Karpelevich boundaries of symmetric spaces. We also consruct some "new" boundaries