Related papers: Symmetric permutation invariants in some tensor pr…

The consideration of tensor products of 0-Hecke algebra modules leads to natural analogs of the Bessel J-functions in the algebra of noncommutative symmetric functions. This provides a simple explanation of various combinatorial properties…

Let $\mathbf{G}$ be either a simple linear algebraic group over an algebraically closed field of positive characteristic or a quantum group at a root of unity. We define new classes of indecomposable $\mathbf{G}$-modules, which we call…

In the previous paper arxiv:math/0610552 semisimple tensor categories were constructed out of certain regular Mal'cev categories. In this paper, we calculate the tensor product multiplicities and the categorical dimensions of the simple…

We investigate tensor products of Hilbert complexes, in particular the (essential) spectrum of their Laplacians. It is shown that the essential spectrum of the Laplacian associated to the tensor product complex is computable in terms of the…

We provide constructions of bent functions using triples of permutations. This approach is due to Mesnager. In general, involutions have been mostly considered in such a machinery; we provide some other suitable triples of permutations,…

In this study, a novel feature coding method that exploits invariance for transformations represented by a finite group of orthogonal matrices is proposed. We prove that the group-invariant feature vector contains sufficient discriminative…

We study infinite products of reproducing kernels with view to their use in dynamics (of iterated function systems), in harmonic analysis, and in stochastic processes. On the way, we construct a new family of representations of the Cuntz…

Lattice gauge theories of permutation groups with a simple topological action (henceforth permutation-TFTs) have recently found several applications in the combinatorics of quantum field theories (QFTs). They have been used to solve…

A theorem of G\"ottsche establishes a connection between cohomological invariants of a complex projective surface $S$ and corresponding invariants of the Hilbert scheme of $n$ points on $S.$ This relationship is encoded in certain infinite…

Consistent tensor products on auxiliary spaces, hereafter denoted "fusion procedures", are defined for general quadratic algebras, non-dynamical and dynamical, inspired by results on reflection algebras. Applications of these procedures…

We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows…

We describe algorithms for computing geometric invariants for Hilbert modular surfaces, and we report on their implementation.

We consider perturbations of dynamical semigroups on the algebra of all bounded operators in a Hilbert space generated by covariant completely positive measures on the semi-axis. The construction is based upon unbounded linear perturbations…

In [Trace identities and $\bf {Z}/2\bf {Z}$-graded invariants, {\it Trans. Amer. Math. Soc. \bf309} (1988), 581--589] we generalized the first and second fundamental theorems of invariant theory from the general linear group to the general…

Although there is no natural internal product for hermitian forms over an algebra with involution of the first kind, we describe how to multiply two $\varepsilon$-hermitian forms to obtain a quadratic form over the base field. This allows…

Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…

We construct a generalization of the theory of symmetric functions involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal…

$O(N)$ invariants are the observables of real tensor models. We use regular colored graphs to represent these invariants, the valence of the vertices of the graphs relates to the tensor rank. We enumerate $O(N)$ invariants as $d$-regular…

We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways. The first…

Well-known operations defined on a non-degenerate inner product vector space are extended to the case of a degenerate inner product. The main obstructions to the extension of these operations to the degenerate case are (1) the index…