Related papers: Lattice invariants from the heat kernel

In this paper, we use a simple discrete dynamical model to study integer partitions and their lattice. The set of reachable configurations of the model, with the order induced by the transition rule defined on it, is the lattice of all…

We construct knot invariants from the radical part of projective modules of restricted quantum groups. We also show a relation between these invariants and the colored Alexander invariants.

We develop the theory of Hermitian Jacobi forms of lattice index, for both definite and indefinite Hermitian lattices. We also prove a theta decomposition theorem for vector-valued Jacobi forms (both in the orthogonal and Hermitian…

We generalize the notion of length to an ordinal-valued invariant defined on the class of finitely generated modules over a Noetherian ring. A key property of this invariant is its semi-additivity on short exact sequences. We show how to…

We define new invariants of knots by means of quandle colorings and longitudinal information. These invariants can be applied to a tangle embedding problem and recognizing non-classical virtual knots.

We propose a lattice counterpart of diffeomorphism symmetry in the continuum. A functional integral for quantum gravity is regularized on a discrete set of space-time points, with fermionic or bosonic lattice fields. When the space-time…

In this work, we study the interlace polynomial as a generalization of a graph invariant to delta-matroids. We prove that the interlace polynomial satisfies the four-term relation for delta-matroids and determines thus a finite type…

We define a modular function which is a generalization of the elliptic modular lambda function. We show this function and the modular invariant function generate the modular function field with respect to the principal congruence subgroup.…

Lattice kinetic equations incorporating the effects of external/internal force fields via a shift of the local fields in the local equilibria, are placed within the framework of continuum kinetic theory. The mathematical treatment reveals…

We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold with 4-singular fibers. We define the Eichler integrals of the modular forms with half-integral weight, and we show that the invariant is rewritten as a sum…

Our earlier results on the temperature inversion properties and the ellipticisation of the finite temperature internal energy on odd spheres are extended to orbifold factors of odd spheres and then to other thermodynamic quantities, in…

We show that Toda lattices with the exceptional Cartan matrices are Liouville type systems. For these systems of equations, we obtain explicit formulas for the invariants and generalized Laplace invariants.

The subfactor approach to modular invariants gives insight into the fusion rule structure of the modular invariants.

A variation of multiple $L$-values, which arises from the description of the special values of the spectral zeta function of the non-commutative harmonic oscillator, is introduced. In some special cases, we show that its generating function…

Let $A$ be a finite or countable alphabet and let $\theta$ be literal (anti)morphism onto $A^*$ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under…

We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as…

The Weyl relations, the harmonic oscillator, the hydrogen atom, the Dirac equation on the lattice are presented with the help of the difference equations and the orthogonal polynomials of discrete variable. This area of research is…

This work comes as the second part in a series of investigations into the dynamics of rotating waves as solutions to lattice dynamical systems. Such nonlinear waves as solutions to mathematical equations are of great interest throughout the…

The first aim of this work is to characterize when the lattice of all submodules of a module is a direct product of two lattices. In particular, which decompositions of a module $M$ produce these decompositions: the \emph{lattice…

Using shift vector method we obtain a large class of self-dual lattices of dimension $(l,l)$, which has a one to one correspondence with modular invariants of free bosonic theory compactified on co-root lattice of a rank $l$ Lie group. Then…