Related papers: Coisotropic Pairs
We give two equivalent sets of invariants which classify pairs of coisotropic subspaces of finite-dimensional Poisson vector spaces. For this it is convenient to dualize; we work with pairs of isotropic subspaces of presymplectic vector…
We identify thirteen isomorphism classes of indecomposable coisotropic relations between Poisson vector spaces and show that every coisotropic relation between finite-dimensional Poisson vector spaces may be decomposed as a direct sum of…
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…
We introduce quantum super-spherical pairs as coideal subalgebras in general linear and orthosymplectic quantum supergroups. These subalgebras play a role of isotropy subgroups for matrices solving $\mathbb{Z}_2$-graded reflection equation.…
A compatible associative algebra is a vector space endowed with two associative multiplication operations that satisfy a natural compatibility condition. In this paper, we investigate and classify compatible pairs of associative algebras of…
We study triples of coisotropic or isotropic subspaces in symplectic vector spaces; in particular, we classify indecomposable structures of this kind. The classification depends on the ground field, which we only assume to be perfect and…
A compatible associative algebra is a vector space equipped with two associative multiplication structures that interact in a certain natural way. This article presents the classification of these algebras with dimension less than four, as…
Let $(b,u)$ be a pair consisting of a symplectic form $b$ on a finite-dimensional vector space $V$ over a field $\mathbb{F}$, and of a $b$-alternating endomorphism $u$ of $V$ (i.e. $b(x,u(x))=0$ for all $x$ in $V$). Let $p$ and $q$ be…
We examine the lattice generated by two pairs of supplementary vector subspaces of a finite-dimensional vector space by intersection and sum, with the aim of applying the results to the study of representations admitting two pairs of…
We define the notion of torically hyperbolic varieties and we construct pair-of-pants decompositions for these in terms of angle sets of essential projective hyperplane complements. This construction generalizes the classical pair-of-pants…
The complement of the codimension 2 complex coordinate subspace arrangement is shown to be homotopy equivalent to a wedge of spheres.
We give an elementary proof of the Pieri-type formula in the cohomology of a Grassmannian of maximal isotropic subspaces of an odd orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of…
We give an alternative argument for the classification of real bundle pairs over smooth symmetric surfaces and extend this classification to nodal symmetric surfaces. We also classify the homotopy classes of automorphisms of real bundle…
In this short note, we classify pairs of conjugacy classes of the symmetric group such that any non-linear irreducible character of the symmetric group vanishes on at least one of them.
We provide a generalization of the normal mode decomposition for non-symmetric or locality constrained situations. This allows for instance to locally decouple a bipartitioned collection of arbitrarily correlated oscillators up to…
We give an elementary proof of the Pieri-type formula in the cohomology of a Grassmannian of maximal isotropic subspaces of an odd orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of…
We establish the leafwise intersection property for closed, coisotropic submanifolds in an exact symplectic manifold satisfying natural additional assumptions.
In this paper we present a complete classification (isomorphism classes with some isomorphism invariants) of complex associative algebras up to dimension five (including both cases: unitary and non-unitary). In some symbolic computations we…
An algebraic isopair is a commuting pair of pure isometries that is annihilated by a polynomial defining a distinguished variety $\mathcal{V}$. The notion of the rank of a pure algebraic isopair with finite bimultiplicity is introduced. For…
We classify the pairwise transitive 2-designs, that is, 2-designs such that a group of automorphisms is transitive on the following five sets of ordered pairs: point-pairs, incident point-block pairs, non-incident point-block pairs,…