相关论文: Symmetry in semidefinite programs
Combinatorial aspects of multivariate diagonal invariants of the symmetric group are studied. As a consequence it is proved the existence of a multivariate extension of the classical Robinson-Schensted correspondence. Further byproduct are…
The symplectic blob algebra is a physically motivated quotient of the Hecke algebra $H(\tilde{C}_n)$ with a diagram calculus. We find the blocks for the symplectic blob algebra for all specialisations of its parameters over the complex…
Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner…
Symmetries of the finite Heisenberg group represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. As is well known, these symmetries are properly expressed in terms of certain normalizer. This…
Regular semisimple Hessenberg varieties are a family of subvarieties of the flag variety that arise in number theory, numerical analysis, representation theory, algebraic geometry, and combinatorics. We give a "Giambelli formula" expressing…
Using the method of equivariant moving frames, we present a procedure for constructing symmetry-preserving finite element methods for second-order ordinary differential equations. Using the method of lines, we then indicate how our…
We study symplectic groups and indefinite orthogonal groups over involutive, possibly noncommutative, algebras $(A, \sigma)$. In the case when the algebra $(A, \sigma)$ is Hermitian, or the complexification $(A_{\mathbb{C}},…
We give necessary and sufficient conditions for the Terwilliger algebra of a quasi-thin Schurian association scheme to coincide with: (a) the centralizer algebra of a point stabilizer of its automorphism group, and (b) its subspace $T^0$.…
This paper delves into the Terwilliger algebra associated with the ordered Hamming scheme, which extends from the wreath product of one-class association schemes and was initially introduced by Delsarte as a natural expansion of the Hamming…
We introduce the notion of Haantjes algebra: It consists of an assignment of a family of operator fields on a differentiable manifold, each of them with vanishing Haantjes torsion. They are also required to satisfy suitable compatibility…
Terwilliger algebras are a subalgebra of a matrix algebra constructed from an association scheme. Rie Tanaka defined what it means for a Terwilliger algebra to be almost commutative and gave five equivalent conditions. In this paper we…
The transparent way for the invariant (Hamiltonian) description of equivariant localization of the integrals over phase space is proposed. It uses the odd symplectic structure, constructed over tangent bundle of the phase space and permits…
For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess…
Methods for the design of physical parameterization schemes that possess certain invariance properties are discussed. These methods are based on different techniques of group classification and provide means to determine expressions for…
These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and…
Symmetry plays a fundamental role in understanding natural phenomena and mathematical structures. This work develops a comprehensive theory for studying the persistent symmetries and degree of asymmetry of finite point configurations over…
We show that the Christensen-Sinclair factorization theorem, when the underlying Hilbert spaces are finite dimensional, is an instance of strong duality of semidefinite programming. This gives an elementary proof of the result and also…
In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite…
In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…
A certain representation for the Heisenberg algebra in finite-difference operators is established. The Lie-algebraic procedure of discretization of differential equations with isospectral property is proposed. Using $sl_2$-algebra based…