Related papers: The Baxter Revolution
Recent results for rotations expressed as polynomials of spin matrices are derived here by elementary differential equation methods. Structural features of the results are then examined in the framework of biorthogonal systems, to obtain an…
Generalized Baxter's relations on the transfer-matrices (also known as Baxter's TQ relations) are constructed and proved for an arbitrary untwisted quantum affine algebra. Moreover, we interpret them as relations in the Grothendieck ring of…
Theory of Rota-Baxter operators on rings and algebras has been developed since 1960. Recently, L. Guo, H. Lang, Y. Sheng [arXiv:2009.03492] have defined the notion of Rota-Baxter operator on a group. We provide some general constructions of…
We give iterative constructions for irreducible polynomials over F_q of degree nt^r for all nonnegative integers r, starting from irreducible polynomials of degree n. The iterative constructions correspond modulo fractional linear…
In this paper we investigate the mathematical properties of the integrability of the symmetric six-vertex model towards the view of Algebraic Geometry. We show that the algebraic variety originated from Baxter's commuting transfer method is…
We construct the Baxter's operator and the corresponding Baxter's equation for a quantum version of the Ablowitz Ladik model. The result is achieved by looking at the quantum analogue of the classical Backlund transformations. For…
This article brings attention to some historical developments that gave rise to the Bayes factor for testing a point null hypothesis against a composite alternative. In line with current thinking, we find that the conceptual innovation - to…
We study the transfer matrix spectral problem for the cyclic representations of the trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov Lax operator. The results apply as well to the spectral analysis of the…
The history of the quadratic stochastic operators can be traced back to work of S.Bernshtein (1924). During more than 80 years this theory developed and many papers were published. In recent years it has again become of interest in…
We present a self-contained discussion of the use of the transfer-matrix formalism to study one-dimensional scattering. We elaborate on the geometrical interpretation of this transfer matrix as a conformal mapping on the unit disk. By…
Quaternions, discovered by Sir William Rowan Hamilton in the 19th century, are a significant extension of complex numbers and a profound tool for understanding three-dimensional rotations. This work explores the quaternion's history,…
Davis and Knuth in 1970 introduced the notion of revolving sequences, as representations of a Gaussian integer. Later, Mizutani and Ito pointed out a close relationship between a set of points determined by all revolving sequences and a…
We revisit the standard representation of the (inverse) Radon transform which is well-known in the mathematical literature. We extend this representation to the case involving the parton distributions. We have found the new additional…
In the past 30 years there have been extensive discoveries in the theory of integrable statistical mechanical models including the discovery of non-linear differential equations for Ising model correlation functions, the theory of random…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
We implement the quantum inverse scattering method for the 4-vertex model. In comparison to previous works of the author which examined the 6-vertex, and 20-vertex, models, the 4-vertex model exhibits different characteristics, ranging from…
The BCS theory injected two powerful ideas into the collective consciousness of theoretical physics: pairing and spontaneous symmetry breaking. In the 50 years since the seminal work of Bardeen, Cooper, and Schrieffer, those ideas have…
We study permutations that are sorted by operators of the form $\mathbf{S} \circ \alpha \circ \mathbf{S}$, where $\mathbf{S}$ is the usual stack sorting operator introduced by D. Knuth and $\alpha$ is any $D_8$-symmetry obtained combining…
Baxter's TQ-equation is solved for the six-vertex model using the representation theory of quantum groups at roots of unity. A novel simplified construction of the Q-operator is given depending on a new free parameter. Specializing this…
The `transcendental methods' in the algebraic theory of quadratic forms are based on two major results, proved in the 60's by Cassels and Pfister, and known as the representation and the subform theorems. A generalization of the…