Related papers: Finite $N$ unitary matrix model
The principle result of this article is the determination of the possible finite subgroups of arithmetic lattices in U(2,1).
We consider N=1 supersymmetric gauge theories based on the group SU(N)_1 x SU(N)_2 x ... x SU(N)_k with matter content (N,N*,1,...,1) + (1,N,N*,..., 1) + >... + (N*,1,1,...,N) as candidates for the unification symmetry of all particles. In…
We compute the large N limit of the partition function of the Euclidean Yang--Mills measure with structure group SU(N) or U(N) on all closed compact surfaces, orientable or not, excepted for the sphere and the projective plane. This limit…
We present a family of matrix models such that their partition functions are tau functions of the universal character (UC) hierarchy. This develops one of the topics of our previous paper arXiv:2410.14823. We found new matrix models…
We report results of two investigations of the double-scaling equations for the unitary matrix models. First, the fixed area partition functions have all positive coefficients only for the first four critical points. This implies that the…
We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…
We study the image of $\textrm{SU}(n)$ under the diagonal product map. Using only elementary tools of linear algebra, analysis and general topology, we find the analytical formula for the boundary of this image and find all special unitary…
A finite or infinite matrix $A$ is image partition regular provided that whenever $\mathbb N$ is finitely colored, there must be some $\vec{x}$ with entries from $\mathbb N$ such that all entries of $A\vec{x}$ are in some color class. In…
We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.
We consider the group M of all polynomial matrices U(z) = U0 + U1*z + U2*z*z +...+Uk*z*...*z, k=0,1,... that satisfy equation U(z)*D*U(z)" = D with the diagonal n*n matrix D=diag{-1,1,1,...1}. Here n > 1, U(z)" = U0" + U1"*z + U2"*z*z +…
In this letter we compute the exact effective superpotential of {\cal N}=1 U(N) supersymmetric gauge theories with N_f fundamental flavors and an arbitrary tree-level polynomial superpotential for the adjoint Higgs field. We use the matrix…
We give an algorithm for computing matrix corepresentations for special linear and special unitary quantum groups using a combinatorial re-indexing of basis elements.
We demonstrate a method for general linear optical networks that allows one to factorize any SU($n$) matrix in terms of two SU($n-1)$ blocks coupled by an SU(2) entangling beam splitter. The process can be recursively continued in an…
A class of matrix models which arises as partition function in U(N) Chern-Simons matter theories on three sphere is investigated. Employing the standard technique of the 1/N expansion we solve the system beyond the planar limit. In…
In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…
The general features of the 1/N expansion in statistical mechanics and quantum field theory are briefly reviewed both from the theoretical and from the phenomenological point of view as an introduction to a more detailed analysis of the…
By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.
An algorithm for computing power conjugate presentations for finite soluble quotients of predetermined structure of finitely presented groups is described. Practical aspects of an implementation are discussed.
In this paper we study the Gan-Gross-Prasad problem for unitary groups over finite fields. Our results provide complete answers for unipotent representations, and we obtain the explicit branching of these representations.
The Cohn-Umans (FOCS '03) group-theoretic framework for matrix multiplication produces fast matrix multiplication algorithms from three subsets of a finite group $G$ satisfying a simple combinatorial condition (the Triple Product Property).…