相关论文: Pentad and triangular structures behind the Racah …
A generalization of the Macdonald polynomials depending upon both commuting and anticommuting variables has been introduced recently. The construction relies on certain orthogonality and triangularity relations. Although many…
We demonstrate how S-matrix poles manifest themselves as the physical spectrum near the upper threshold in the context of the two-channel uniformized Mittag-Leffler expansion, an expression written as a sum of pole terms under an…
A two-channel problem is considered within a method based on first order differential equations that are equivalent to the corresponding Schr\"odinger equation but are more convenient for dealing with resonant phenomena. Using these…
Rigged configurations are combinatorial objects prominent in the study of solvable lattice models. Marginally large tableaux are semi-standard Young tableaux of special form that give a realization of the crystals ${\cal B}(\infty)$. We…
We provide a systematic approach to describing the Ramond-Ramond (RR) fields as elements in twisted differential K-theory. This builds on a series of constructions by the authors on geometric and computational aspects of twisted…
Webs are planar graphs with boundary that describe morphisms in a diagrammatic representation category for $\mathfrak{sl}_k$. They are studied extensively by knot theorists because braiding maps provide a categorical way to express link…
Racks and quandles are rich algebraic structures that are strong enough to classify knots. Here we develop several fundamental categorical aspects of the theories of racks and quandles and their relation to the theory of permutations. In…
A general construction is given for a class of invertible maps between the classical $U(sl(2))$ and the Jordanian $U_{h}(sl(2))$ algebras. Different maps are directly useful in different contexts. Similarity trasformations connecting them,…
The symmetric group $S_6$ that permutes the six five-fold axes of an icosahedron is introduced to go beyond the simple rotations that constitute the icosahedral group $I$. Owing to the correspondence $h\leftrightarrow d$, the calculation of…
We define a lattice statistical model on a triangulated manifold in four dimensions associated to a group $G$. When $G=SU(2)$, the statistical weight is constructed from the $15j$-symbol as well as the $6j$-symbol for recombination of…
Links and knots are exotic topological structures that have garnered significant interest across multiple branches of natural sciences. Coherent links and knots, such as those constructed by phase or polarization singularities of coherent…
A skew polynomial ring $R=K[x;\sigma,\delta]$ is a ring of polynomials with non-commutative multiplication. This creates a difference between left and right divisibility, and thus a concept of left and right evaluations and roots. A…
The algebra of monodromy matrices for sl(n) trigonometric R-matrices is studied. It is shown that a generic finite-dimensional polynomial irreducible representation of this algebra is equivalent to a tensor product of L-operators.…
Let $A$ be an algebra over a commutative ring $k$. We introduce the notion of a coquasitriangular left bialgebroid over $A$ and show that the category of left comodules over such a bialgebroid has a braiding. We also investigate a Tannaka…
This paper concerns a stochastic construction of probabilistic coherent spaces by employing novel ingredients (i) linear exponential comonads arising properly in the measure-theory (ii) continuous orthogonality between measures and…
The spectroscopic properties of an open quantum system are determined by the eigenvalues and eigenfunctions of an effective Hamiltonian H consisting of the Hamiltonian H_0 of the corresponding closed system and a non-Hermitian correction…
Motivated by applications to perverse sheaves, we study combinatorics of two cell decompositions of the symmetric product of the complex line, refining the complex stratification by multiplicities. Contingency matrices, appearing in…
The intricate network of interactions observed in RNA three-dimensional structures is often described in terms of a multitude of geometrical properties, including helical parameters, base pairing/stacking, hydrogen bonding and backbone…
The Rankin--Cohen brackets provide a basic example of ``non-elementary" differential symmetry breaking operators. They can be interpreted as bi-differential operators remarkable for reflecting the structure of fusion rules for holomorphic…
For two-component assemblies, an inherent structure diagram (ISD) is the relationship between set inter-subunit energies and the types of kinetic traps (inherent structures) one may obtain from those energies. It has recently been shown…