Related papers: Determinants for integral forms in lattice type ve…
We prove a transformation formula relating two determinants involving elliptic shifted factorials. Similar determinants have been applied to multiple elliptic hypergeometric series.
A notion of intermediate vertex subalgebras of lattice vertex operator algebras is introduced, as a generalization of the notion of principal subspaces. Bases and the graded dimensions of such subalgebras are given.As an application, it is…
We present a direct approach for the calculation of functional determinants of the Laplace operator on balls. Dirichlet and Robin boundary conditions are considered. Using this approach, formulas for any value of the dimension, $D$, of the…
We consider the five-vertex model on a finite square lattice with fixed boundary conditions such that the configurations of the model are in a one-to-one correspondence with the boxed plane partitions (3D Young diagrams which fit into a box…
The object of this paper is to investigate the certain results involving Bateman's matrix polynomials for integral index. We obtain some properties, integral representation and recurrence relations for hypergeometric matrix function. We…
The irreducible modules of the 2-cycle permutation orbifold models of lattice vertex operator algebras of rank 1 are classified, the quantum dimensions of irreducible modules and the fusion rules are determined.
We generalize the (signed) Varchenko matrix of a hyperplane arrangement to complexes of oriented matroids and show that its determinant has a nice factorization. This extends previous results on hyperplane arrangements and oriented…
The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid. It also presents the construction of a horizontal Laplace operator…
In this expository note, we compute the exact value of the norm of the resolvent of the Volterra operator.
This work builds on Varchenko et al's introduction of bilinear forms for hyperplane arrangements, where the determinant of the associated matrices factorizes into simple components. While one of the determinant formula developed by…
An integral formula is developed which applies to an essentially arbitrary function. An application is made to the Riemann zeta function.
We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.
Explicit determinant formulas are presented for the $\tau$ functions of the generalized Painlev\'e equations of type $A$. This result allows an interpretation of the $\tau$-functions as the Pl\"ucker coordinates of the universal Grassmann…
We give an index formula for elliptic differential operators whose coefficients include shifts forming an infinite group.
This is a continuation of our work to understand vertex operator algebras using the geometric properties of varieties attached to vertex operator algebras. For a class of vertex operator algebras including affine vertex operator algebras…
In this paper we consider Jacobi forms of half-integral index for any positive definite lattice L (classical Jacobi forms from the book of Eichler and Zagier correspond to the lattice A_1=<2>). We give a lot of examples of Jacobi forms of…
Using techniques from the theory of mock modular forms and harmonic Maass forms, especially Weierstrass mock modular forms, we establish several dimension formulas for certain strongly rational, holomorphic vertex operator algebras,…
Under binary matrices we mean matrices whose entries take one of two values. In this paper, explicit formulae for calculating the determinant of some type of binary Toeplitz matrices are obtained. Examples of the application of the…
The notion of the characteristic Lie algebra of the discrete hyperbolic type equation is introduced. An effective algorithm to compute the algebra for the equation given is suggested. Examples and further applications are discussed.
A compound determinant identity for minors of rectangular matrices is established. As an application, we derive Vandermonde type determinant formulae for classical group characters.