Related papers: Inner Product in Highest-Weight Representation
We classify integrable irreducible highest weight representations of non-twisted affine Lie superalgebras. We give a free field construction in the level~1 case. The analysis of this construction shows, in particular, that in the simplest…
The paper presents an interesting mathematical feedback between the formalism of coherent states and the field of integrals and integral representations involving special functions. This materializes through an easy and fast method to…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
The computational cost of solving an inverse problem governed by PDEs, using multiple experiments, increases linearly with the number of experiments. A recently proposed method to decrease this cost uses only a small number of random linear…
Let $\mathfrak{g}$ be a symmetrizable Kac-Moody Lie algebra and let $\rho$ denote the sum of the fundamental weights. The irreducible highest weight representations $V(m\rho)$ occupy a distinguished position in representation theory due to…
The Iwahori-Hecke algebra of type A acts on tensor product space of the natural representation of the quantum superalgebra U_q(gl(m,n)). We show this action of the Hecke algebra and the action of U_q(gl(m,n)) on the same space determine…
We show how to construct relevant families of matrix product operators in one and higher dimensions. Those form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In…
We present a novel framework for learning cost-efficient latent representations in problems with high-dimensional state spaces through nonlinear dimension reduction. By enriching linear state approximations with low-order polynomial terms…
Let $A(1):=k[X]/(X^p)$ be the natural representation of the Witt algebra $W(1)$ over an algebraically closed field of prime characteristic $p>3$. In this note, we decompose the $W(1)$-module $A(1)\otimes A(1)$ into two invariant subspaces,…
This work is devoted to the study Translation-Invariant (TI) Matrix Product State (MPS) representations of quantum states with periodic boundary conditions (PBC). We pursue two directions: we introduce new methods for constructing TI MPS…
We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets.…
We describe an algorithm for computing the complete set of primitive orthogonal idempotents in the centralizer ring of the permutation representation of a wreath product. This set of idempotents determines the decomposition of the…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
Motivated by the problem of filtering candidate pairs in inner product similarity joins we study the following inner product estimation problem: Given parameters $d\in {\bf N}$, $\alpha>\beta\geq 0$ and unit vectors $x,y\in {\bf R}^{d}$…
We consider a large class of series of symmetrizable Kac-Moody algebras (generically denoted X_n). This includes the classical series A_n as well as others like E_n whose members are of Indefinite type. The focus is to analyze the behavior…
We propose $\textit{weighted inner product similarity}$ (WIPS) for neural network-based graph embedding. In addition to the parameters of neural networks, we optimize the weights of the inner product by allowing positive and negative…
The task of changing the overlap between two quantum states can not be performed by making use of a unitary evolution only. However, by means of a unitary-reduction process it can be probabilistically modified. Here we study in detail the…
This research provides a formal definition of the arithmetic theta lift for cusp forms of weight $3/2$ and establishes the arithmetic inner product formula, thereby completing the Kudla program on modular curves. This formula is…
In this paper, we present a formalism for representing infinite systems in quantum mechanics by employing a strategy that embraces divergences rather than avoiding them. We do this by representing physical quantities such as inner products,…