Related papers: Matrix models for noncommutative algebraic manifol…
Tensor models are generalizations of matrix models, and are studied as discrete models of quantum gravity for arbitrary dimensions. Among them, the canonical tensor model (CTM for short) is a rank-three tensor model formulated as a totally…
We show the problem of counting homomorphisms from the fundamental group of a homology $3$-sphere $M$ to a finite, non-abelian simple group $G$ is #P-complete, in the case that $G$ is fixed and $M$ is the computational input. Similarly,…
We present a new class of hermitian one-matrix models originated in the W-infinity algebra: more precisely, the polynomials defining the W-infinity generators in their fermionic bilinear form are shown to expand the orthogonal basis of a…
We evidence a family $\mathcal{X}$ of square matrices over a field $\mathbb{K}$, whose elements will be called X-matrices. We show that this family is shape invariant under multiplication as well as transposition. We show that $\mathcal{X}$…
Let G be a real, connected, noncompact, semisimple Lie group, let K be a maximal compact subgroup of G, and let g=k+p be the corresponding Cartan decomposition of the complexified Lie algebra of G. Sequences of strongly orthogonal…
For certain rings $\mathcal{R}$, we construct explicit matrices representing nonzero classes in the algebraic $K$ theory group $NK_{1}(\mathcal{R})$.
This article resides in the realm of the noncommutative (free) analog of real algebraic geometry - the study of polynomial inequalities and equations over the real numbers - with a focus on matrix convex sets $C$ and their projections $\hat…
We consider the quantum inverse scattering method for several mixed integrable models based on the rational SU(N) R-matrix with general toroidal boundary conditions. This includes systems whose Hilbert spaces are invariant by the discrete…
A matrix algebra is constructed which consists of the necessary degrees of freedom for a finite approximation to the algebra of functions on the family of orthogonal Grassmannians of real dimension 2N, known as complex quadrics. These…
Let X be the moduli space of SL(n,C), SU(n), GL(n,C), or U(n)-valued representations of a rank r free group. We classify the algebraic singular stratification of X. This comes down to showing that the singular locus corresponds exactly to…
Theory of matrix factorizations is useful to study hypersurfaces in commutative algebra. To study noncommutative hypersurfaces, which are important objects of study in noncommutative algebraic geometry, we introduce a notion of…
We construct quasi-solvable quantum mechanical matrix models by employing two different methods, the one is universal enveloping algebra of Lie superalgebra and the other is N-fold supersymmetry. For the former we examine the q(2) and…
In N=1 supersymmetric SO(N)/USp(2N) gauge theories with the tree-level superpotential W(\Phi) that is an arbitrary polynomial of the adjoint matter \Phi, the massless fluctuations about each quantum vacuum are described by U(1)^n gauge…
In this paper many classes of sets of matrices with entries in F (F=R, F=C, F=H) are introduced. Each class with the corresponding topology determines a real analytical, complex or symplectic manifold for F=R, F=C or F=H respectively. Any…
In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking values in the…
Given a nilpotent Lie group $N$, a compact subgroup $K$ of automorphisms of $N$ and an irreducible unitary representation $(\tau,W_\tau)$ of $K$, we study conditions on $\tau$ for the commutativity of the algebra of…
Given a quantum subgroup $G\subset U_n$ and a number $k\leq n$ we can form the homogeneous space $X=G/(G\cap U_k)$, and it follows from the Stone-Weierstrass theorem that $C(X)$ is the algebra generated by the last $n-k$ rows of coordinates…
A unitary matrix model is proposed as the large-N matrix formulation of M theory on flat space with toroidal topology. The model reproduces the motion of elementary D-particles on the compact space, and admits membrane states with nonzero…
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
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…