Y. Neretin

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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 $I^\pm ⩽ n$ be positive integers. Consider the general linear group $GL (I^\pm + n, F_{q})$ and its subgr…

math.RT2025

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

Yury A. Neretin

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

math.RT2025

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.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…