Related papers: Simple harmonic oscillators from non-semisimple wa…
The walled Brauer algebras $B_N(m,n)$ govern Schur--Weyl duality for unitary groups $U(N)$ acting on mixed tensor spaces $V_N^{\otimes m}\otimes \overline{V}_N^{\otimes n}$ and play an important role in applications ranging from AdS/CFT to…
We study the representation theory of the rook-Brauer algebra RB_k(x), also called the partial Brauer algebra. This algebra has a basis of "rook-Brauer" diagrams, which are Brauer diagrams that allow for the possibility of missing edges.…
We construct combinatorial (involutory) Gelfand models for the following diagram algebras in the case when they are semi-simple: Brauer algebra, its partial analogue, walled Brauer algebra, its partial analogue, Temperley-Lieb algebra, its…
This paper studies the combinatoric structure of the set of all representations, up to equivalence, of a finite-dimensional semisimple Lie algebra. This has intrinsic interest as a previously unsolved problem in representation theory, and…
We consider operators acting on a UMD Banach lattice $X$ that have the same algebraic structure as the position and momentum operators associated with the harmonic oscillator $-\frac12\Delta + \frac12|x|^{2} $ acting on…
The variational wave functions based on neural networks have recently started to be recognized as a powerful ansatz to represent quantum many-body states accurately. In order to show the usefulness of the method among all available…
Transformation coefficients between standard bases for irreducible representations of the Brauer centralizer algebra $\mathfrak{B}_f(x)$ and split bases adapted to the $\mathfrak{B}_{f_1} (x) \times \mathfrak{B}_{f_2} (x) \subset…
The fundamental building blocks in band theory are band representations (BRs): bands whose infinitely-numbered Wannier functions are generated (by action of a space group) from a finite number of symmetric Wannier functions centered on a…
The gauge invariant degrees of freedom of matrix models based on an N x N complex matrix, with U(N) gauge symmetry, contain hidden free particle structures. These are exhibited using triangular matrix variables via the Schur decomposition.…
We give a full nonlinear numerical treatment of time-dependent 5d braneworld geometry, which is determined self-consistently by potentials for the scalar field in the bulk and at two orbifold branes, supplemented by boundary conditions at…
In this paper we study the partial Brauer $\mathbb{C}$-algebras $\mathfrak{R}_n(\delta,\delta')$, where $n \in \mathbb{N}$ and $\delta,\delta'\in\mathbb{C}$. We show that these algebras are generically semisimple, construct the Specht…
The success of any machine learning system depends critically on effective representations of data. In many cases, it is desirable that a representation scheme uncovers the parts-based, additive nature of the data. Of current representation…
Machine learning representations of many-body quantum states have recently been introduced as an ansatz to describe the ground states and unitary evolutions of many-body quantum systems. We explore one of the most important representations,…
In this paper we discuss representations of the Birman-Wenzl-Murakami algebra as well as of its dilute extension containing several free parameters. These representations are based on superalgebras and their baxterizations permit us to…
We describe a new technique to obtain representations of the braid group B_n from the R-matrix of a quantum deformed algebra of the one dimensional harmonic oscillator. We consider the action of the R-matrix not on the tensor product of…
We study rotating wave solutions of the nonlinear wave equation $$ \left\{ \begin{aligned} \partial_{t}^2 v - \Delta v + m v & = |v|^{p-2} v \quad && \text{in $\mathbb{R} \times \mathbf{B}$} \\ v & = 0 && \text{on $\mathbb{R} \times…
A unitary representation of a, possibly infinite dimensional, Lie group G is called semi-bounded if the corresponding operators id\pi(x) from the derived representations are uniformly bounded from above on some non-empty open subset of the…
We investigate application of the nonlinearity management (NM, i.e., periodic variation of the strength of the inter-component repulsion) to the miscibility-immiscibility (MIM) transition across the critical point of a two-component BEC,…
We provide an algorithm for calculating the unramified Brauer group of a homogeneous space $X$ of a semi-simple simply connected group $H$ with finite geometric stabiliser over any field of characteristic 0. When $k$ is a number field, we…
It was shown in arXiv:2309.10786 that the leading non-perturbative contribution to the large $N$ expansion of superconformal index of (2,0) 6d theory (which describes low-energy dynamics of $N$ coincident M5 branes) is reproduced by the…