相关论文: On subfactors arising from asymptotic representati…
We give a complete list of indecomposable characters of the infinite symmetric semigroup. In comparison with the analogous list for the infinite symmetric group, one should introduce only one new parameter, which has a clear combinatorial…
The theory of subfactors of groups, together with the associated notions of subindices and index stability for groupsandtheirsubsets, hasrecentlybeenintroducedandsystematicallydeveloped. Theseconceptsexhibitdeepconnections with additive…
We will describe the relationship between the indecomposable characters of the finitary symmetric group and its ergodic invariant random subgroups; and we will interpret each Thoma character as an asymptotic limit of a naturally associated…
Recently, sub-indices and sub-factors of groups with connections to number theory, additive combinatorics, and factorization of groups have been introduced and studied. Since all group subsets are considered in the theory and there are many…
We simplify construction of Thoma representations of an infinite symmetric group
We classify the subvarieties of infinite dimensional affine space that are stable under the infinite symmetric group. We determine the defining equations and point sets of these varieties as well as the containments between them.
We provide a family of group measure space II_1 factors for which all finite index subfactors can be explicitly listed. In particular, the set of all indices of irreducible subfactors can be computed. Concrete examples show that this index…
We construct irreducible hyperfinite subfactors of index 6 with a prescribed fundamental group from a large family containing all countable and many uncountable subgroups of R_+. We also prove that there are unclassifiably many irreducible…
A theorem is derived which (i) provides a new class of subfactors which may be interpreted as generalized asymptotic subfactors, and which (ii) ensures the existence of two-dimensional local quantum field theories associated with certain…
The number of subgroups and the number of cyclic subgroups are natural combinatorial invariants of a finite group. We investigate how restrictions on these quantities, together with the number of distinct prime divisors of $|G|$, enforce…
To any complex Hadamard matrix H one associates a spin model commuting square, and therefore a hyperfinite subfactor. The standard invariant of this subfactor captures certain "group-like" symmetries of H. To gain some insight, we compute…
We define a metric ultraproduct of topological groups with left-invariant metric, and show that there is a countable sequence of finite groups with left-invariant metric whose metric ultraproduct contains isometrically as a subgroup every…
Subfactor standard invariants encode quantum symmetries. The small index subfactor classification program has been a rich source of interesting quantum symmetries. We give the complete classification of subfactor standard invariants to…
For numerical semigroups with a specified list of (not necessarily minimal) generators, we obtain explicit asymptotic expressions, and in some cases quasipolynomial/quasirational representations, for all major factorization length…
The symmetric inverse monoid $I_X$ on a set $X$ consists of all bijective functions whose domain and range are subsets of $X$ under the usual composition and inversion of partial functions. For an arbitrary infinite set $X$, we classify all…
A subgroup $H$ of a finite group $G$ is submodular in $G$ if there is a subgroup chain $H=H_0\leq\ldots\leq H_i\leq H_{i+1}\leq \ldots \leq H_n=G$ such that $H_i$ is a modular subgroup of $H_{i+1}$ for every $i$. We investigate finite…
The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory - harmonic analysis for noncommutative groups with infinite-dimensional dual space. I omitted detailed proofs but tried…
For any abstract subfactor planar algebra $P$, there exists a finite index extremal subfactor $M_0 \subset M_1$ with $P$ as its standard invariant. In this paper, we classify the automorphism group of a bipartite graph planar algebra, and…
Indecomposible semifinite harmonic functions on the direct product of graded graphs are classified. As a particular case, the full list of indecomposible traces for the infinite inverse symmetric semigroup is obtained.
A group is SimpHAtic if it acts geometrically on a simply connected simplicially hereditarily aspherical (SimpHAtic) complex. We show that finitely presented normal subgroups of the SimpHAtic groups are either: finite, or of finite index,…