Related papers: A Difference Formula for Tensor-power Multipliciti…
We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A-G based on the explicit construction of weight states. This straightforward approach (which is slower and more…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
Using our previous results on the systematic construction of invariant differential operators for non-compact semisimple Lie groups we classify the special reduced multiplets and minimal representations in the case of SO(p,q).
We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not…
We study tensors on Lie groupoids suitably compatible with the groupoid structure, called {\em multiplicative}. Our main result gives a complete description of these objects only in terms of infinitesimal data. Special cases include the…
In this paper we study the representation theory of the algebras generated by the single bond transfer matrices in dilute lattice models. This representation theory is related to a tensor product of monoidal categories. This construction is…
We present a framework for constructing strong mixed-integer programming formulations for logical disjunctive constraints. Our approach is a generalization of the logarithmically-sized formulations of Vielma and Nemhauser for SOS2…
We introduce a class of strongly \'{e}tale difference algebras, whose role in the study of difference equations is analogous to the role of \'{e}tale algebras in the study of algebraic equations. We deduce an improved version of Babbitt's…
We give a presentation of the centralizer algebras for tensor products of spinor representations of quantum groups via generators and relations. In the even-dimensional case, this can be described in terms of non-standard q-deformations of…
We propose a new operator defined between two tensors, the broadcast product. The broadcast product calculates the Hadamard product after duplicating elements to align the shapes of the two tensors. Complex tensor operations in libraries…
We construct a cellular basis of the walled Brauer algebra which has similar properties as the Murphy basis of the group algebra of the symmetric group. In particular, the restriction of a cell module to a certain subalgebra can be easily…
Taking inspiration from the work of Lanphier \cite{LANPHIER2022125716}, a generalized multivariable polynomial formulation for sums of alternating powers is given, as well as analogous sums. Furthermore, an analog of the Euler-Maclaurin…
We introduce a representation theory of q-Lie algebras defined earlier in \cite{DG1}, \cite{DG2}, formulated in terms of braided modules. We also discuss other ways to define Lie algebra-like objects related to quantum groups, in…
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…
Unlike the classical polynomial case there has not been invented up to very recently a tool similar to the Bernstein-Bezier representation which would allow us to control the behavior of the exponential polynomials. The exponential analog…
We give an exact coefficients formula of any infinite product of power series with constant term equal to $1$, by using structures from partitions of integers and permutation groups. This is an universal theorem for various of Binomial-type…
The reappearance of a sometimes called exotic behavior for linear and multilinear pseudodifferential operators is investigated. The phenomenon is shown to be present in a recently introduced class of bilinear pseudodifferential operators…
We apply some recent developments of Baldoni-Beck-Cochet-Vergne on vector partition function, to Kostant's and Steinberg's formulae, for classical Lie algebras $A\_r$, $B\_r$, $C\_r$, $D\_r$. We therefore get efficient {\tt Maple} programs…
A fully tensorial theoretical framework for hypercomplex-valued neural networks is presented. The proposed approach enables neural network architectures to operate on data defined over arbitrary finite-dimensional algebras. The central…
Polynomial algebra offers a standard approach to handle several problems in geometric modeling. A key tool is the discriminant of a univariate polynomial, or of a well-constrained system of polynomial equations, which expresses the…