Related papers: Reflection operator and hypergeometry II: $SL(2, \…
We study the general solution of the Yang-Baxter equation with deformed $sl(2)$ symmetry. The universal R operator acting on tensor products of arbitrary representations is obtained in spectral decomposition and in integral forms. The…
Combining recent results by A. Macinic, S. Papadima and R. Popescu with a spectral sequence and computer aided computations, we determine the monodromy action on $H^1(F,\mathbb{C})$, where $F$ denotes the Milnor fiber of the hyperplane…
In a system with an even number of SU(2) spins, there is an overcomplete set of states--consisting of all possible pairings of the spins into valence bonds--that spans the S=0 Hilbert subspace. Operator expectation values in this basis are…
We study the broken ray transform on $n$-dimensional Euclidean domains where the reflecting parts of the boundary are flat and establish injectivity and stability under certain conditions. Given a subset $E$ of the boundary $\partial…
We study normal reflection subgroups of complex reflection groups. Our approach leads to a refinement of a theorem of Orlik and Solomon to the effect that the generating function for fixed-space dimension over a reflection group is a…
Let S be a symmetric relation with deficiency index (1,1). In this article, we extend Krein`s resolvent formalism in order to describe all, not necessarily self-adjoint, extensions $S \subset \tilde{A}$ with $\varrho(\tilde{A})\neq…
We employ the light-cone superspace formalism to develop an efficient approach to constructing superconformal operators of twist two in Yang-Mills theories with N=1,2,4 supercharges. These operators have an autonomous scale dependence to…
We construct a class of negative spin irreducible representations of the su(2) Lie algebra. These representations are infinite-dimensional and have an indefinite inner product. We analyze the decomposition of arbitrary products of positive…
Eigenfunctions of the Askey-Wilson second order $q$-difference operator for $0<q<1$ and $|q|=1$ are constructed as formal matrix coefficients of the principal series representation of the quantized universal enveloping algebra…
In this paper, we assume that all isoparametric submanifolds have flat section. The main purpose of this paper is to prove that, if a full irreducible complete isoparametric submanifold of codimension greater than one in a symmetric space…
We calculate the spectrum and a basis of eigenvectors for the Spin Dirac operator over the standard 3-sphere. For the spectrum, we use the method of Hitchin which we transfer to quaternions and explain in more detail. The eigenbasis (in…
We consider a general statistical mechanics model on a product of local spaces and prove that, if the corresponding measure is reflection positive, then several site-monotonicity properties for the two-point function hold. As an application…
The spectral decomposition for an explicit second-order differential operator $T$ is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with…
The weak operator topology closed operator algebra on $L^2(R)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $exp(i\lambda x), \lambda \geq 0$, is shown to be a reflexive operator algebra, in the…
A universal minimal spinor set of linear differential equations describing anyons and ordinary integer and half-integer spin fields is constructed with the help of deformed Heisenberg algebra with reflection. The construction is generalized…
In the first section we provide a solution to the M. G. Krein problem about an inner description of the space $L_2(\Sigma,H).$ In the second section we introduce the multiplicity function for an operator measure. Making use of the…
We study the spectrum of the linear operator $L = - \partial_{\theta} - \epsilon \partial_{\theta} (\sin \theta \partial_{\theta})$ subject to the periodic boundary conditions on $\theta \in [-\pi,\pi]$. We prove that the operator is closed…
The author studies the structure of space $ \mathbf {L} _ {2} (G) $ of vector-valued functions that are square integrable in a bounded connected domain $ G $ of the three-dimensional space with a smooth boundary and the role of gradient…
Group elements of SU(2) are expressed in closed form as finite polynomials of the Lie algebra generators, for all definite spin representations of the rotation group. The simple explicit result exhibits connections between group theory,…
A continuous linear operator L defined on the space of entire functions H(C) is said to be an extended $lambda$-eigenoperator of the differentiation operator D provided DL = $lambda$LD. Here we fully characterize when an extended…