Y. Neretin

activity

19972026

most citedThe Lagrangian Radon Transform and the Weil representation

30 citations · 178 across the 55 of their papers we have counts for

collaborators

66 papers

math.CA2026

Spherical harmonics, operators of multiplication by coordinates, and infinitesimal conformal transformations

Yury A. Neretin

Consider the space of $C^{\infty}$ -functions on the two-dimensional sphere $S^{2}$ and its decomposition $\oplus H_{n}$ into a direct sum of minimal rotation-invariant spaces. We…

math.RT2026

On a super-Virasoro group, a semigroup of annuli, and Gauss--Berezin integral operators

Yury A. Neretin

Denote by $A$ the Grassmann algebra with a countable number of generators, by $A_{0}$ , $A_{1}$ its even and odd parts. We consi…

math.RT2025

On algebras of conjugacy classes of symmetric groups with respect to Young subgroups

Yury A. Neretin

We consider the subalgebra of the group algebra of a symmetric group consisting of functions that are constant on conjugacy classes with respect to a Young subgroup. We write an ex…

math.RT2025

One algebra of double cosets for a general linear group over a finite field

Yury A. Neretin

Let $F_{q}$ be finite field with $q$ elements. Let $α ⩽ n$ be positive integers. Consider the general linear group $GL (α + n, F_{q})$ and its subgrou…

math.RT2025

Algebra of double cosets of a symmetric group by a smaller symmetric group

Yury A. Neretin

Fix a natural $α$ . Let $n \geq α$ be an integer. Consider the symmetric group $S_{α + n}$ and its subgroup $S_{n}$ . We consider the group algebra of $S_{α + n}$ and its subalgebra $\mathbb…

math.RT2025

Some remarks on the group of formal diffeomorphisms of the line

Yury A. Neretin

Consider a strictly positively graded finitely generated infinite-dimensional real Lie algebra $g$ . It has a well-defined Lie group $G$ , which is an…

math.GR2025

On visualisation of completions of free groups

Yury A. Neretin

Our purpose is to visualize the pronilpotent completion of a finitely generated free group as a certain subgroup in the free Lie group.

math.HO2024

The double gamma function and Vladimir Alekseevsky

Yury A. Neretin

This paper is about a forgotten function and a forgotten mathematician. The double gamma function is now an important special function, which appears for different reasons in many…

math.RT2023

Oligomorphic groups, categories of partial bijections, and ultrahomogeneous cubic spaces over finite fields

Yury A. Neretin

We show that for certain class of oligomorphic groups there is a version of multiplication of double cosets in the Ismagilov--Olshanski sense. Categories of (reduced) double cosets…

math.RT2023

On Derkachov--Manashov $R$ -matrices for the principal series of unitary representations

Yury A. Neretin

In 2001--2013 Derkachov and Manashov with coauthors obtained simple and natural expressions of $R$ -matrices for the principal series of representations of the groups $\mathrm{SL}(2…

math.GR2023

On the group of homeomorphisms of the Basilica

Yury A. Neretin

We show that the group of all homeomorphisms of the Basilica fractal coincides with a group of transformations of a certain non-locally finite ribbon tree. Also, we show that Basil…

math.DS2023★ 1 cited

Non-singular actions of infinite-dimensional groups and polymorphisms

Yury A. Neretin

Let $Z$ be a probabilistic measure space with a measure $ζ$ , $R^{\times}$ be the multiplicative group of positive reals, let $t$ be the coordinate on $R^{\times}$ . A…

math.RT2022

Groups of isometries of ultrametric Urysohn spaces and their unitary representations

Yury A. Neretin

We consider groups $I$ of isometries of ultrametric Urysohn spaces $U$ . Such spaces $U$ admit transparent realizations as boundaries of certain $R$ -trees…

math.CA2022★ 3 cited

On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions

Yury A. Neretin

The Selberg integral has a twin (`the Dotsenko--Fateev integral') of the following form. We replace real variables $x_{k}$ in the integrand $\prod |x_k|^{σ-1}\,|1-x_k|^{τ-1} \prod|x_…

math.RT2022

Virtual permutations and polymorhisms

Yury A. Neretin

There is a natural map from a symmetric group $S_{n}$ to a smaller symmetric group $S_{n - 1}$ , we write a decomposition of a permutation into a product of disjoint cycles and remove t…

math.CV2021

Inner functions of matrix argument and conjugacy classes in unitary groups

Yury A. Neretin

Denote by $B_{n}$ the set of complex square matrices of order $n$ , whose Euclidean operator norms are $< 1$ . Its Shilov boundary is the set $U (n)$ of all unitary matrices. A holomorph…

math.CA2021

On a $C^{2}$ -valued integral index transform and bilateral hypergeometric series

Yury A. Neretin

We discuss the spectral decomposition of the hypergeometric differential operators on the line $Re z = 1/2$ . Such operators arise in the problem of decomposition of tensor…

math.RT2021★ 1 cited

Some remarks on traces on the infinite-dimensional Iwahori--Hecke algebra

Yury A. Neretin

The infinite-dimensional Iwahori--Hecke algebras $H_{\infty} (q)$ are direct limits of the usual finite-dimensional Iwahori--Hecke algebras. They arise in a natural way as c…

math.GR2020★ 1 cited

On double cosets of groups $G L (n)$ with respect to subgroups of block strictly triangular matrices

Yury A. Neretin

We parametrize the space of double cosets of the group $G L (n, k)$ with respect to two subgroups $T_{-}$ , $T_{+}$ of block strictly triangular matrices. In Addendum, we consider the…

math.RT2020

Fourier transform on the Lobachevsky plane and operational calculus

Yury A. Neretin

The classical Fourier transform on the line sends the operator of multiplication by $x$ to $i \frac{d}{d ξ}$ and the operator of differentiation $\frac{d}{d x}$ to the multiplication…

math.FA2020

Polyhomomorphisms of locally compact groups

Yury A. Neretin

Let $G$ and $H$ be locally compact groups with fixed two-side-invariant Haar measures. A polyhomomorphism $G \to H$ is a closed subgroup $R \subset G \times H$ with a fixed Haar measu…

math.RT2020★ 2 cited

Groups $G L (\infty)$ over finite fields and multiplications of double cosets

Yury A. Neretin

Let $F$ be a finite field. Consider a direct sum $V$ of an infinite number of copies of $F$ , consider the dual space $V^{⋄}$ , i.~e., the direct product of an i…

math.HO2019

Kolmogorov reform of mathematical education, 1970-1980

Yury A. Neretin

This reform was a part of a transnational movement as 'the New Math' in the United States or the activity of the Lichnerowicz commission in France. The Russian version of these eve…

math.CA2019★ 17 cited

Barnes-Ismagilov integrals and hypergeometric functions of the complex field

Yury A. Neretin

We examine a family $_{p} G_{q}^{C} [( b ) ( a ); z]$ of integrals of Mellin-Barnes type over the space $Z \times R$ , such functio…

Spherical harmonics, operators of multiplication by coordinates, and infinitesimal conformal transformations

On a super-Virasoro group, a semigroup of annuli, and Gauss--Berezin integral operators

On algebras of conjugacy classes of symmetric groups with respect to Young subgroups

One algebra of double cosets for a general linear group over a finite field

Algebra of double cosets of a symmetric group by a smaller symmetric group

Some remarks on the group of formal diffeomorphisms of the line

On visualisation of completions of free groups

The double gamma function and Vladimir Alekseevsky

Oligomorphic groups, categories of partial bijections, and ultrahomogeneous cubic spaces over finite fields

On Derkachov--Manashov R-matrices for the principal series of unitary representations

On the group of homeomorphisms of the Basilica

Non-singular actions of infinite-dimensional groups and polymorphisms

Groups of isometries of ultrametric Urysohn spaces and their unitary representations

On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions

Virtual permutations and polymorhisms

Inner functions of matrix argument and conjugacy classes in unitary groups

On a C2-valued integral index transform and bilateral hypergeometric series

Some remarks on traces on the infinite-dimensional Iwahori--Hecke algebra

On double cosets of groups GL(n) with respect to subgroups of block strictly triangular matrices

Fourier transform on the Lobachevsky plane and operational calculus

Polyhomomorphisms of locally compact groups

Groups GL(∞) over finite fields and multiplications of double cosets

Kolmogorov reform of mathematical education, 1970-1980

Barnes-Ismagilov integrals and hypergeometric functions of the complex field

On Derkachov--Manashov $R$ -matrices for the principal series of unitary representations

On a $C^{2}$ -valued integral index transform and bilateral hypergeometric series

On double cosets of groups $G L (n)$ with respect to subgroups of block strictly triangular matrices

Groups $G L (\infty)$ over finite fields and multiplications of double cosets