Related papers: on lagrangian-grassmannian variety
We use a recently found method to characterise all the invertible fourth-order difference equations linear in the extremal values based on the existence of a discrete Lagrangian. We also give some result on the integrability properties of…
The stratification of the Grassmannian by positroid varieties has been the subject of extensive research. Positroid varieties are in bijection with a number of combinatorial objects, including $k$-Bruhat intervals and bounded affine…
Recent results on the Grassmannian perspective of soliton equations with an elliptic spectral parameter are presented along with a detailed review of the classical case with a rational spectral parameter. The nonlinear Schr\"odinger…
The graph of a real symplectic linear transformation is an R-Lagrangian subspace of a complex symplectic vector space. The restriction of the complex symplectic form is thus purely imaginary and may be expressed in terms of the generating…
We investigate the Exact Renormalization Group (ERG) description of ($Z_2$ invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show…
Hierarchies of Lagrangians of degree two, each only partly determined by the choice of leading terms and with some coefficients remaining free, are considered. The free coefficients they contain satisfy the most general differential…
The geometric Lagrangian theory (of arbitrary order) is based on the analysis of some basic mathematical objects such as: the contact ideal, the (exact) variational sequence, the existence of Euler-Lagrange and Helmholtz-Sonin forms, etc.…
Lagrangian curves in 4-space entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic…
We initiate a systematic construction of real analytic Lagrangian fibrations from integer matrices. We prove that when the matrix is of full column rank, the perverse filtration associated with the Lagrangian fibration matches the mixed…
In this paper we relate a well-known in symplectic geometry compactification of the space of symmetric bilinear forms considered as a chart of the Lagrangian Grassmannian to the specific compactifications of the space of electrical networks…
We elaborate on the recently proposed Lagrangian parent formulation. In particular, we identify a natural choice of the allowed field configurations ensuring the equivalence of the parent and the starting point Lagrangians. We also analyze…
Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are…
In this paper we postulate an algebraic model to explain how the symmetry of three lepton species plays its role in the Lorentz extension. Inspired by the two-to-one mapping between the group SL (2, C) and the Lorentz group, we design a…
Let g be a Lie algebra over an algebraically closed field of characteristic p>0 and let U(g) be the universal enveloping algebra of g. We prove in this paper that for g=gl_n and g=sl_n the centre of U(g) is a unique factorisation domain and…
We show that modeling a Grassmannian as symmetric orthogonal matrices $\operatorname{Gr}(k,\mathbb{R}^n) \cong\{Q \in \mathbb{R}^{n \times n} : Q^{\scriptscriptstyle\mathsf{T}} Q = I, \; Q^{\scriptscriptstyle\mathsf{T}} = Q,\;…
We introduce a new method to construct a large family of Lagrangian surfaces in complex Euclidean plane by means of two planar curves making use of their usual product as complex functions and integrating the Hermitian product of their…
We describe an iterative construction of Lagrangian tori in the complex Grassmannian $\operatorname{Gr}(k,n)$, based on the cluster algebra structure of the coordinate ring of a mirror Landau-Ginzburg model proposed by Marsh-Rietsch. Each…
It has been an open problem to find the Moore-Penrose inverses of the incidence, Laplacian, and signless Laplacian matrices of families of graphs except trees and unicyclic graphs. Since the inverse formulas for an odd unicyclic graph and…
We speculate on Dyson series for the $S$-matrix when the interaction depends on derivatives of the fields. We stick on two particular examples: the scalar electrodynamics and the renormalised $\phi ^4$ theory. We eventually give evidence…
We study the Lagrangian isotopy classification of Lagrangian spheres in the Milnor fibre, $B_{d,p,q}$, of the cyclic quotient surface T-singularity $\frac{1}{dp^2} (1,dpq-1)$. We prove that there is a finitely generated group of…