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We study the holomorphic twist of 3d N = 2 supersymmetric field theories, discuss the perturbative bulk local operators in general, and explicitly construct non perturbative bulk local operators for abelian gauge theories. Our construction…
The Laguerre functions constitute one of the fundamental basis sets for calculations in atomic and molecular electron-structure theory, with applications in hadronic and nuclear theory as well. While similar in form to the Coulomb…
We present explicit generators of an algebra of commuting difference operators with trigonometric coefficients. The operators are simultaneously diagonalized by recently discovered q-polynomials (viz. Koornwinder's multivariable…
An algorithm is described to convert Lorentz and gauge invariant expressions in non--Abelian gauge theories with matter into a standard form, consisting of a linear combination of basis invariants. This algorithm is needed for computer…
Within the concept of a non-Archimedean operator algebra with the Baer reduction (A. N. Kochubei, On some classes of non-Archimedean operator algebras, Contemporary Math. 596 (2013), 133--148), we consider algebras of operators on Banach…
In this paper, we introduce twisted Rota-Baxter operators on Lie algebras as an operator analogue of twisted r-matrices. We construct a suitable $L_\infty$-algebra whose Maurer-Cartan elements are given by twisted Rota-Baxter operators.…
We develop different formulas of algebraic and/or arithmetic nature allowing an explicit calculation, both over a finite field and over a field of characteristic 0, of the algebraic part of the unramified Brauer group of a homogeneous space…
We give a Riemann-Hilbert approach to the theory of matrix orthogonal polynomials. We will focus on the algebraic aspects of the problem, obtaining difference and differential relations satisfied by the corresponding orthogonal polynomials.…
In this paper, we give a generic algorithm of the transition operators between Hermitian Young projection operators corresponding to equivalent irreducible representations of SU(N), using the compact expressions of Hermitian Young…
The extension of the noncommutative u*(N) Lie algebra to noncommutative orthogonal and symplectic Lie algebras is studied. Using an anti-automorphism of the star-matrix algebra, we show that the u*(N) can consistently be restricted to o*(N)…
This paper investigates the homology of the Brauer algebras, interpreted as appropriate Tor-groups, and shows that it is closely related to the homology of the symmetric group. Our main results show that when the defining parameter of the…
In this paper, for a smooth variety equiped with an action of a connected algebraic group (not necessary linear), we introduce the notion of invariant Brauer sub-group and the notion of invariant \'etale Brauer-Manin obstruction. Then we…
This paper is a sequel to "Computing diagonal form and Jacobson normal form of a matrix using Groebner bases", J. of Symb. Computation, 46 (5), 2011. We present a new fraction-free algorithm for the computation of a diagonal form of a…
The Adler-Kostant-Symes $R$-bracket scheme is applied to the algebra of pseudo-differential operators to relate the three integrable hierarchies: KP and its two modifications, known as nonstandard integrable models. All three hierarchies…
Picture changed operators are discussed in $N=2$ strings with space-time signature $(2,2)$. A gauge symmetry algebra is derived in a background of torus space-time $T^{2,2}$ and its simple representation on the picture changed operators is…
The purpose of this paper is to introduce the cohomology and deformations of twisted Rota-Baxter operators on 3-Leibniz algebras and NS-3-Leibniz algebras. We construct an $L_\infty$-algebra whose Maurer-Cartan elements are twisted…
A formulation of quantum mechanics with additive and multiplicative (q-)difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding…
Gauge-invariant boundary conditions in Euclidean quantum gravity can be obtained by setting to zero at the boundary the spatial components of metric perturbations, and a suitable class of gauge-averaging functionals. This paper shows that,…
We completely characterize Birkhoff-James orthogonality with respect to numerical radius norm in the space of bounded linear operators on a complex Hilbert space. As applications of the results obtained, we estimate lower bounds of…
In previous two papers, we defined fractional Brauer configuration algebras and developed their covering theory. In this paper, we study the representation theory of fractional Brauer graph algebras of type MS, a special class of fractional…