Related papers: Congruence invariants of matrix mutation

By studying modular invariance properties of some characteristic forms, we get some new anomaly cancellation formulas on $(4r-1)$ dimensional manifolds. As an application, we derive some results on divisibilities of the index of Toeplitz…

We use methods of the general theory of congruence and *congruence for complex matrices--regularization and cosquares-to determine a unitary congruence canonical form (respectively, a unitary *congruence canonical form) for complex matrices…

We describe "quasi canonical modules" for modular invariant rings $R$ of finite group actions on factorial Gorenstein domains. From this we derive a general "quasi Gorenstein criterion" in terms of certain 1-cocycles. This generalizes a…

We consider random matrices that have invariance properties under the action of unitary groups (either a left-right invariance, or a conjugacy invariance), and we give formulas for moments in terms of functions of eigenvalues. Our main tool…

We show that the quasiequational theory of a relatively congruence modular quasivariety of left $R$-modules is determined by a two-sided ideal in $R$ together with a filter of left ideals. The two-sided ideal encodes the identities that…

We comment two papers of Domokos and Vaccarino proving that the restriction to diagonal matrices of the scheme of commuting matrices is an isomorphism when restricted to invariants to the symmetric group invariants.

It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…

We prove wall-crossing formulas for the motivic invariants of the moduli spaces of framed objects in the ind-constructible abelian categories. Developed techniques are applied in the case of the motivic Donaldson-Thomas invariants of…

Let G be a compact, connected Lie group, acting smoothly on a manifold M. Goresky-Kottwitz-MacPherson described a small Cartan model for the equivariant cohomology of M, quasi-isomorphic to the standard Cartan complex of equivariant…

In this work we derive important properties regarding matrix invariants which occur in the theory of differential equations with reflection.

In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.

Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…

We publish a table of primitive finite-type invariants of order less than or equal to six, for knots of ten or fewer crossings. We note certain mod-2 congruences, one of which leads to a chirality criterion in the Alexander polynomial. We…

We give in this paper which is the fifth in a series of eight a theory of covariant derivatives of multivector and extensor fields based on the geometric calculus of an arbitrary smooth manifold M, and the notion of a connection extensor…

To every $k$-dimensional modular invariant vector space we associate a modular form on $SL(2,\mathbb{Z})$ of weight $2k$. We explore number theoretic properties of this form and find a sufficient condition for its vanishing which yields…

In the present paper we construct differential invariants for generic rank 2 vector distributions on n-dimensional manifold. In the case n=5 (the first case containing functional parameters) E. Cartan found in 1910 the covariant…

This paper investigates the relation between Toda brackets and congruences of modular forms. It determines the $f$-invariant of Toda brackets and thereby generalizes the formulas of J.F.\ Adams for the classical $e$-invariant to the…

In previous work, the authors have each introduced methods for studying the 2-line of the p-local Adams-Novikov spectral sequence in terms of the arithmetic of modular forms. We give the precise relationship between the congruences of…

In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…

We introduce a notion of quasi-lisse vertex algebras, which generalizes admissible affine vertex algebras. We show that the normalized character of an ordinary module over a quasi-lisse vertex operator algebra has a modular invariance…