Related papers: On compositions with $x^2/(1-x)$
A system of multivariate formal power series $\varphi$ with a homogeneous decomposition $\varphi=\sum_{k=0}^\infty\varphi_k$ is invertible under composition if $\varphi_0=0$ and $\mathrm{det}(\varphi_1)\ne 0.$ All invertible series over a…
Let V be an even dimensional vector space over a field K of characteristic 2 equipped with a non-degenerate alternating bilinear form f. The divided power algebra DV is considered as a complex with differential defined from f. We examine…
A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semibounded if the corresponding operators $i\dd\pi(x)$ from the derived representation are uniformly bounded from above on some non-empty open subset of…
We study two types of series over a real alternative $^*$-algebra $A$. The first type are series of the form $\sum_{n} (x-y)^{\punto n}a_n$, where $a_n$ and $y$ belong to $A$ and $(x-y)^{\punto n}$ denotes the $n$--th power of $x-y$ w.r.t.\…
We generalize the Umbral Calculus of G-C. Rota by studying not only sequences of polynomials and inverse power series, or even the logarithms studied in, but instead we study sequences of formal expressions involving the iterated logarithms…
Given an affine Poisson algebra, that is singular one may ask whether there is an associated symplectic form. In the smooth case the answer is obvious: for the symplectic form to exist the Poisson tensor has to be invertible. In the…
Zonotopal algebra deals with ideals and vector spaces of polynomials that are related to several combinatorial and geometric structures defined by a finite sequence of vectors. Given such a sequence X, an integer k>=-1 and an upper set in…
Ordinary algebra of formal power series in one variable is convenient to study by means of the algebra of Riordan matrices and the Riordan group. In this paper we consider algebra of formal power series without constant term, isomorphic to…
We associate to each $r$-multigraded, locally finitely generated ideal in the "large polynomial ring" on countably many indeterminates a power series in $r$ variables; this power series is the limit in the adic topology of the numerators of…
We study a class of algebras with non-Lie commutation relations whose symplectic leaves are surfaces of revolution: a cylinder or a torus. Over each of such surfaces we introduce a family of complex structures and Hilbert spaces of…
For a commutative algebra which comes from a Zinbiel algebra the exponential series can be written without denominators. When lifted to dendriform algebras this new series satisfies a functional equation analogous to the…
A condition is identified which guarantees that the coinvariants of a coaction of a Hopf algebra on an algebra form a subalgebra, even though the coaction may fail to be an algebra homomorphism. A Hilbert Theorem (finite generation of the…
An FI- or an OI-module $\mathbf{M}$ over a corresponding noetherian polynomial algebra $\mathbf{P}$ may be thought of as a sequence of compatible modules $\mathbf{M}_n$ over a polynomial ring $\mathbf{P}_n$ whose number of variables depends…
We prove that when $q$ is a power of $2$, every complex irreducible representation of $\mathrm{Sp}(2n, \mathbb{F}_q)$ may be defined over the real numbers, that is, all Frobenius-Schur indicators are 1. We also obtain a generating function…
There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt…
The power structure over the Grothendieck (semi)ring of complex quasi-projective varieties constructed by the authors is used to express the generating series of classes of Hilbert schemes of zero-dimensional subschemes on a smooth…
Let F be a p-adic field of odd residual characteristic. Let G(n) and G`(n) be the metaplectic double covers of the general symplectic group and the symplectic group attached to the 2n dimensional symplectic space over F. Let T be a genuine,…
We study representations of finite groups on Stanley--Reisner rings of simplicial complexes and on lattice points in lattice polytopes. The framework of translative group actions allows us to use the theory of proper colorings of simplicial…
This paper is a study of power series, where the coefficients are binomial expressions (iterated finite differences). Our results can be used for series summation, for series transformation, or for asymptotic expansions involving Stirling…
We study symplectic structures on characteristically nilpotent Lie algebras (CNLAs) by computing the cohomology space $H^2(\Lg,k)$ for certain Lie algebras $\Lg$. Among these Lie algebras are filiform CNLAs of dimension $n\le 14$. It turns…