Related papers: Towards plethystic $\mathfrak{sl}_2$ crystals
This work develops a new method, based on the use of Gustafson's integrals and on the evaluation of singular integrals, allowing one to establish the unitarity of the separation of variables transform for infinite-dimensional…
Motivated by work of the first author, this paper studies symplectic embedding problems of lagrangian products that are sufficiently symmetric. In general, lagrangian products arise naturally in the study of billiards. The main result of…
We present a complex matrix gauge model defined on an arbitrary two-dimensional orientable lattice. We rewrite the model's partition function in terms of a sum over representations of the group U(N). The model solves the general…
Let $K$ be a number field, let $A$ be a finite-dimensional $K$-algebra, let $\mathrm{J}(A)$ denote the Jacobson radical of $A$, and let $\Lambda$ be an $\mathcal{O}_{K}$-order in $A$. Suppose that each simple component of the semisimple…
Emerging sampling algorithms based on normalizing flows have the potential to solve ergodicity problems in lattice calculations. Furthermore, it has been noted that flows can be used to compute thermodynamic quantities which are difficult…
Taylor expansion of the thermodynamic potential in powers of the (baryo)chemical potential $\mu_B$ is a well-known method to bypass the Sign Problem of Lattice QCD. Due to the difficulty in calculating the higher order Taylor coefficients,…
A non-perturbative algebraic theory of lattice Boltzmann method is developed based on a symmetry of a product. It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which…
We derive group branching laws for formal characters of subgroups $H_\pi$ of GL(n) leaving invariant an arbitrary tensor $T^\pi$ of Young symmetry type $\pi$ where $\pi$ is an integer partition. The branchings $GL(n)\downarrow GL(n-1)$,…
There exist a number of well known multiplicative generating functions for series of Schur functions. Amongst these are some related to the dual Cauchy identity whose expansion coefficients are rather simple, and in some cases periodic in…
A lattice Boltzmann scheme is presented which recovers the dynamics of nematic and chiral liquid crystals; the method essentially gives solutions to the Qian-Sheng equations for the evolution of the velocity and tensor order-parameter…
While there has been some progress on the decomposition of Kronecker products of characters of the symmetric groups in recent times, results on the symmetric and alternating part of Kronecker squares are still scarce. Here, new results (and…
We develop a topological method of measuring Chern-Simons number change in the real time evolution of classical lattice SU(2) and SU(2) Higgs theory. We find that the Chern-Simons number diffusion rate per physical 4-volume is very heavily…
Decays of unstable heavy particles usually involve the coherent sum of several amplitudes, like in a multiple slit experiment. Dedicated amplitude analysis techniques have been widely used to resolve these amplitudes for better…
A detailed combinatorial analysis of planar lattice convex polygonal lines is presented. This makes it possible to answer an open question of Vershik regarding the existence of a limit shape when the number of vertices is constrained. The…
Solving crystal structures from kinematical X-ray or electron diffraction patterns of single crystals requires many more diffracted beams to be recorded than there are atoms in the structure, since the phases of the structure factors can…
In part I: We find a series physical scales such as 1) Planck scale, 2) Minimal approximate grand unification SU(5), 3) the mass scale of the see saw model right handed or Majorana neutrinoes, some invented scale with many scalar bosons,…
We present several methods, which utilize symplectic integration techniques based on two and three part operator splitting, for numerically solving the equations of motion of the disordered, discrete nonlinear Schr\"odinger (DDNLS)…
Lattice gauge theory simulations are our principal probe of the masses of the light quarks. Results from such computations are the primary evidence against the $m_u=0$ solution to the strong CP problem. The large-$N$ approximation offers an…
In this paper, we enumerate the pairs of permutations that are long cycles and whose product has a given cycle-type. Our main result is a simple relation concerning the desired numbers for a few related cycle-types. The relation refines a…
We consider two division problems on narrow strips of square and hexagonal lattices. In both cases we compute the bivariate enumerating sequences and the corresponding generating functions, which allowed us to determine the asymptotic…