Related papers: Invariant and Group Theoretical Integrations over …

Integrals for the product of unitary-matrix elements over the U(n) group will be discussed. A group-theoretical formula is available to convert them into a multiple sum, but unfortunately the sums are often tedious to compute. In this…

This paper presents a powerfull method to integrate general monomials on the classical groups with respect to their invariant (Haar) measure. The method has first been applied to the orthogonal group in [J. Math. Phys. 43, 3342 (2002)], and…

I adapt a recently introduced method for integrating over the unitary group (S. Aubert and C.S. Lam, J.Math.Phys. 44, 6112-6131 (2003)) to the orthogonal group. I derive explicit formulas for a number of one, two and three-vector integrals,…

A recursion formula is derived which allows to evaluate invariant integrals over the orthogonal group O(N), where the integrand is an arbitrary finite monomial in the matrix elements of the group. The value of such an integral is…

We consider integrals of type $\int_{O_n}u_{11}^{a_1}... u_{1n}^{a_n}u_{21}^{b_1}... u_{2n}^{b_n} du$, with respect to the Haar measure on the orthogonal group. We establish several remarkable invariance properties satisfied by such…

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…

We present a method to calculate integrals over monomials of matrix elements with invariant measures in terms of Wick contractions. The method gives exact results for monomials of low order. For higher--order monomials, it leads to an error…

We apply a novel method for the equivalence group and its infinitesimal generators to the investigation of invariants of linear ordinary differential equations. First, a comparative study of this method is illustrated by an example. Next,…

We investigate the existence problem of group invariant matrices using algebraic approaches. We extend the usual concept of multipliers to group rings with cyclotomic integers as coefficients. This concept is combined with the field descent…

A constructive version of the Frobenius integrability theorem -- that can be programmed effectively -- is given. This is used in computing invariants of groups of low ranks and recover examples from a recent paper of Boyko, Patera and…

We stress the potential usefulness of renormalization group invariants. Especially particular combinations thereof could for instance be used as probes into patterns of supersymmetry breaking in the MSSM at inaccessibly high energies. We…

In our earlier article~\cite{CanSakran} we initiated a study of the complement-finite submonoids of the group of integer points of a unipotent linear algebraic group. In the present article, we continue to develop tools and techniques for…

Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…

Grouping has been commonly used in deep metric learning for computing diverse features. However, current methods are prone to overfitting and lack interpretability. In this work, we propose an improved and interpretable grouping method to…

We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.

We introduce a new method to evaluate algebraic integrals over the simplex numerically. This new approach employs techniques from tropical geometry and exceeds the capabilities of existing numerical methods by an order of magnitude. The…

This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…

We develop a new, group-theoretic approach to bounding the exponent of matrix multiplication. There are two components to this approach: (1) identifying groups G that admit a certain type of embedding of matrix multiplication into the group…

Here we develop a technique of computing the invariants of $n-$ary forms and systems of forms using the discriminants of corresponding multilinear forms built of their partial derivatives, which should be cosidered as analogues of classical…

This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…