Related papers: Effective Invariant Theory of Permutation Groups u…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
The main purpose of this paper is to develop new algorithms for computing invariant rings in a general setting. This includes invariants of nonreductive groups but also of groups acting on algebras over certain rings. In particular, we…
An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.
Let $G$ be a complex classical group, and let $V$ be its defining representation (possibly plus a copy of the dual). A foundational problem in classical invariant theory is to write down generators and relations for the ring of…
We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…
Using evaluation at appropriately chosen points, we propose a Gr\"obner basis free approach for calculating the secondary invariants of a finite permutation group. This approach allows for exploiting the symmetries to confine the…
The group algebra of the permutation group is spanned by a set of elements called projectors. The coordinates of permutations expanded in projectors are matrix elements of irreducible representations. The projectors of the permutation group…
In this paper we give a Casimir Invariant for the Symmetric group $S_n$. Furthermore we obtain and present, for the first time in the literature, explicit formulas for the matrices of the standard representation in terms of the matrices of…
A very classical subject in Commutative Algebra is the Invariant Theory of finite groups. In our work on 3-dimensional topology (S. King, Ideal Turaev-Viro invariants. To appear in Top. Appl.), we found certain examples of group actions on…
Many finite groups, including all finite non-abelian simple groups, can be symmetrically generated by involutions. In this paper we give an algorithm to symmetrically represent elements of finite groups and to transform symmetrically…
In this article it is determined which integral reflection representations of the symmetric groups and the primitive complex reflection groups of degree $2$ have rings of invariants which are isomorphic to polynomial rings.
We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…
The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \emph{basic invariants}. In particular, we set out to find the set of…
We introduce a method to design a computationally efficient $G$-invariant neural network that approximates functions invariant to the action of a given permutation subgroup $G \leq S_n$ of the symmetric group on input data. The key element…
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…
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…
We initiate a study of the rings of invariants of modular representations of elementary abelian p-groups. With a few notable exceptions, the modular representation theory of an elementary abelian p-group is wild. However, for a given…
In this paper we study invariant rings arising in the study of finite dimensional algebraic structures. The rings we encounter are graded rings of the form $K[U]^{\Gamma}$ where $\Gamma$ is a product of general linear groups over a field…
Group algebras of permutations have proved highly useful in solving a number of problems in large N gauge theories. I review the use of permutations in classifying gauge invariants in one-matrix and multi-matrix models and computing their…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…