Related papers: Normal form for the walled Brauer algebra: constru…
We present a way to associate an algebra $B_G (\Upsilon) $ with every pseudo reflection group $G$. When $G$ is a Coxeter group of simply-laced type we show $B_G (\Upsilon)$ is isomorphic to the generalized Brauer algebra of simply-laced…
In this paper we provide novel results on the infinite level normal form and orbital normal form classifications of nonlinear Eulerian and rotational vector fields with two pairs of non-resonant imaginary modes. We use the method of…
We give formal normal forms for parabolic logarithmic transseries $f=z+\cdots \, $, with respect to parabolic logarithmic normalizations. Normalizations are given algorithmically, using fixed point theorems, as limits of Picard's sequences…
Explicit formulas for the symmetrizer and the antisymmetrizer of the Birman-Wenzl-Murakami algebras BWM(r,q)_n are given.
Here is discussed application of the Weyl pair to construction of universal set of quantum gates for high-dimensional quantum system. An application of Lie algebras (Hamiltonians) for construction of universal gates is revisited first. It…
Some more general "inheritance conditions" have been found for a given set of symmetry generators $\{\mathbf{Z}_{\bar{l}}\}$ acting on some set of coupled ordinary differential equations, once the "first integration method" has been applied…
We classify canonical algebras such that for every dimension vector of a regular module the corresponding module variety is normal (respectively, a complete intersection). We also prove that for the dimension vectors of regular modules…
We provide explicit and unified formulae for the normalized 3-cocycles on arbitrary finite abelian groups. As an application, we compute all the braided monoidal structures on linear Gr-categories.
The aim of this short note is to show how to construct a rationnal Remmert reduction for the universal cover of a smooth K\"ahler orbifold. Doins this, we are led to introduce some singular K\"ahler metrics adapted to the orbifold…
We give a general expression for the normally ordered form of a function F(w(a,a*)) where w is a function of boson annihilation and creation operators satisfying [a,a*]=1. The expectation value of this expression in a coherent state becomes…
Defined by Borel, a real number is normal to an integer base $b$, greater than or equal to $2$, if in its base-$b$ expansion every block of digits occurs with the same limiting frequency as every other block of the same length. We consider…
We give algorithms for computing multiplier ideals using Gr\"obner bases in Weyl algebras. The algorithms are based on a newly introduced notion which is a variant of Budur--Musta\c{t}\v{a}--Saito's (generalized) Bernstein--Sato polynomial.…
We define a normal graph algebra modeled on algebras used in genetics. Although the algebra does not always determine its graph, it often highlights special features. After developing basic properties of the algebra, we examine those of…
Let $R$ be an associative unital algebra over a field $k,$ let $p$ be an element of $R,$ and let $R'=R\langle q\mid pqp= p\rangle.$ We obtain normal forms for elements of $R',$ and for elements of $R'$-modules arising by extension of…
We first introduce the Wigner-Weyl-Moyal formalism for a theory whose phase-space is an arbitrary Lie algebra. We also generalize to quantum Lie algebras and to supersymmetric theories. It turns out that the non-commutativity leads to a…
We define geodesic normal forms for the general series of complex reflection groups G(de,e,n). This requires the elaboration of a combinatorial technique in order to determine minimal word representatives and to compute the length of the…
We describe various diagram algebras and their representation theory using cellular algebras of Graham and Lehrer and the decomposition into half diagrams. In particular, we show the diagram algebras surveyed here are all cellular algebras…
We describe how traceless projection of tensors of a given rank can be constructed in a closed form. On the way to this goal we invoke the representation theory of the Brauer algebra and the related Schur-Weyl dualities. The resulting…
We present an efficient algorithm for computing the leading monomials of a minimal Groebner basis of a generic sequence of homogeneous polynomials. Our approach bypasses costly polynomial reductions by exploiting structural properties…
For any grading by an abelian group $G$ on the exceptional simple Lie algebra $\mathcal{L}$ of type $E_6$ or $E_7$ over an algebraically closed field of characteristic zero, we compute the graded Brauer invariants of simple…