Related papers: Reflexponents
We classify bireflectional elements (products of 2 involutions) in symplectic groups Sp$(2n, K)$ over a field $K$. We also classify rev ersible elements (elements conjugate to their inverses) and bireflectional elements in finite projective…
Groupoids graded by the groupoid of bijections between finite sets admit generating functions which encode the groupoid cardinalities of their graded components. As suggested in the work of Baez and Dolan, we use analytic continuation of…
We construct natural symbolic representations of intrinsically ergodic, but not necessarily expansive, principal algebraic actions of countably infinite amenable groups and use these representations to find explicit generating partitions…
Let $K$ be a compact group, and let $\rho$ be a representation of $K$ on a Hilbert space $\mathcal{H}_\rho$. We classify invariant subspaces of $\mathcal{H}_\rho$ in terms of range functions, and investigate frames of the form $\{\rho(\xi)…
We describe the rings of invariants for the finite orthogonal groups of plus type in odd characteristic acting on the defining representations. We also describe the invariants of the corresponding Sylow subgroups in the defining…
Functional bases of second-order differential invariants of the Euclid, Poincar\'e, Galilei, conformal, and projective algebras are constructed. The results obtained allow us to describe new classes of nonlinear many-dimensional invariant…
Moment invariants are a powerful tool for the generation of rotation-invariant descriptors needed for many applications in pattern detection, classification, and machine learning. A set of invariants is optimal if it is complete,…
We define a new invariant of finitely generated representations of a finite group, with coefficients in a commutative noetherian ring. This invariant uses group cohomology and takes values in the singularity category of the coefficient…
We construct families of finitely presented groups exhibiting new divergence behavior; we obtain divergence functions of the form $r^\alpha$ for a dense set of exponents $\alpha \in [2,\infty)$ and $r^n\log(r)$ for integers $n \geq 2$. The…
We enumerate several classes of pattern-avoiding rectangulations. We establish new bijective links with pattern-avoiding permutations, prove that their generating functions are algebraic, and confirm several conjectures by Merino and…
Given a morphism of (small) groupoids with injective object map, we provide sufficient and necessary conditions under which the induction and co-induction functors between the categories of linear representations are naturally isomorphic. A…
The strong isomorphism classes of extensions of finite groups are parametrized by orbits of a prescribed action on the second cohomology group. We study these orbits in the case of extensions of a finite abelian $p$-group by a cyclic factor…
In this paper, we study a composition of exponential generating functions. We obtain new properties of this composition, which allow to distinguish prime numbers from composite numbers. Using the result of paper we get the known properties…
Classical invariant theory of a complex reflection group $W$ highlights three beautiful structures: -- the $W$-invariant polynomials constitute a polynomial algebra, over which -- the $W$-invariant differential forms with polynomial…
We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models. In continuation and completion of our earlier work, we present two…
V.F. Molchanov considered the Hilbert series for the space of invariant skew-symmetric tensors and dual tensors with polynomial coefficients under the action of a real reflection group, and speculated that it had a certain product formula…
We show how to derive new instances of the cyclic sieving phenomenon from old ones via elementary representation theory. Examples are given involving objects such as words, parking functions, finite fields, and graphs.
A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating…
We identify those elements of the homeomorphism group of the circle that can be expressed as a composite of two involutions.
It is shown that, in the 1-jet space of the circle, the swapping and the flyping procedures, which produce topologically equivalent links, can produce nonequivalent legendrian links. Each component of the links considered is legendrian…