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

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35 papers · 1 filter

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.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.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.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.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.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.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.RT2019

On the group of spheromorphisms of the homogeneous non-locally finite tree

Yury A. Neretin

Consider a tree $T$ , all whose vertices have countable valence; its boundary is the Baire space $B ≃ N^{N}$ ; continued fractions expansions id…

math.RT2019

Description of unitary representations of the group of infinite $p$ -adic integer matrices

Yury A. Neretin

We classify irreducible unitary representations of the group of all infinite matrices over a $p$ -adic field ( $p \neq = 2$ ) with integer elements equipped with a natural topology. Any i…

math.RT2019★ 1 cited

On the group of infinite $p$ -adic matrices with integer elements

Yury A. Neretin

Let $G$ be an infinite-dimensional real classical group containing the complete unitary group (or complete orthogonal group) as a subgroup. Then $G$ generates a category of double…

math.RT2019★ 2 cited

On spherical unitary representations of groups of spheromorphisms of Bruhat--Tits trees

Yury A. Neretin

Consider an infinite homogeneous tree $T_{n}$ of valence $n + 1$ , its group $A u t (T_{n})$ of automorphisms, and the group $H i e (T_{n})$ of its spheromorphisms (hierarchomorphisms), i.~e., th…

math.RT2018

Operational calculus for Fourier transform on the group $G L (2, R)$

Yury A. Neretin

Consider the Fourier transform on the group $G L (2, R)$ of real $2 \times 2$ -matrices. We show that Fourier-images of polynomial differential operators on $G L (2, R)$ are differential-d…

math.RT2018★ 4 cited

After Plancherel formula

Yury A. Neretin

We discuss two topics related to Fourier transforms on Lie groups and on homogeneous spaces: the operational calculus and the Gelfand--Gindikin problem (program) about separation o…

math.RT2017★ 2 cited

Symmetric groups and checker triangulated surfaces

Yury A. Neretin

We consider triangulations of surfaces with edges painted three colors so that edges of each triangle have different colors. Such structures arise as Belyi data (or Grothendieck de…

math.RT2017★ 1 cited

Projectors separating spectra for $L^{2}$ on symmetric spaces $GL(n,\C)/GL(n,\R)$

Yury A. Neretin

The Plancherel decomposition of $L^{2}$ on a pseudo-Riemannian symmetric space $G L (n, C) / G L (n, R)$ has spectrum of $[n /2]$ types. We write explicitly orthogonal projectors separating s…

math.RT2017

Projectors separating spectra for $L^{2}$ on pseudounitary groups $U (p, q)$

Yury A. Neretin

The spectrum of $L^{2}$ on a pseudo-unitary group $U (p, q)$ (we assume $p \geq q$ naturally splits into $q + 1$ types. We write explicitly orthogonal projectors in $L^{2}$ to subspaces with…

math.RT2017★ 3 cited

On the Weil representation of infinite-dimensional symplectic group over a finite field

Yury A. Neretin

We extend the Weil representation of infinite-dimensional symplectic group to a representation a certain category of linear relations.

math.RT2015★ 8 cited

Restriction of representations of $G L (n + 1, C)$ to $G L (n, C)$ and action of the Lie overalgebra

Yury A. Neretin

Consider a restriction of an irreducible finite dimensional holomorphic representation of $\GL(n+1,C)$ to the subgroup $G L (n, C)$ (it is determined by the Gelfand-Tsetlin branching…

math.RT2015

Infinite symmetric groups and combinatorial constructions of topological field theory type

Yury A. Neretin

The paper contains a survey of train constructions for infinite symmetric groups and related groups. For certain pairs (a group $G$ , a subgroup $K$ ), we construct categories, whose…

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

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

Groups of isometries of ultrametric Urysohn spaces and their unitary representations

Virtual permutations and polymorhisms

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

Fourier transform on the Lobachevsky plane and operational calculus

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

On the group of spheromorphisms of the homogeneous non-locally finite tree

Description of unitary representations of the group of infinite p-adic integer matrices

On the group of infinite p-adic matrices with integer elements

On spherical unitary representations of groups of spheromorphisms of Bruhat--Tits trees

Operational calculus for Fourier transform on the group GL(2,R)

After Plancherel formula

Symmetric groups and checker triangulated surfaces

Projectors separating spectra for L2 on symmetric spaces $GL(n,\C)/GL(n,\R)$

Projectors separating spectra for L2 on pseudounitary groups U(p,q)

On the Weil representation of infinite-dimensional symplectic group over a finite field

Restriction of representations of GL(n+1,C) to GL(n,C) and action of the Lie overalgebra

Infinite symmetric groups and combinatorial constructions of topological field theory type

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

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

Description of unitary representations of the group of infinite $p$ -adic integer matrices

On the group of infinite $p$ -adic matrices with integer elements

Operational calculus for Fourier transform on the group $G L (2, R)$

Projectors separating spectra for $L^{2}$ on symmetric spaces $GL(n,\C)/GL(n,\R)$

Projectors separating spectra for $L^{2}$ on pseudounitary groups $U (p, q)$

Restriction of representations of $G L (n + 1, C)$ to $G L (n, C)$ and action of the Lie overalgebra