The representation theory of infinite wreath product groups is developed by means of the relationship between their group algebras and conjugacy classes with those of the infinite symmetric group. Further, since these groups are inductive limits of finite groups, their finite characters can be classified as limits of normalized irreducible characters of prelimit finite groups. This identificati...

Convergent infinite products, indexed by all natural numbers, in which each factor is a rational function of the index, can always be evaluated in terms of finite products of gamma functions. This goes back to Euler. A purpose of this note is to demonstrate the usefulness of this fact through a number of diverse applications involving multiplicative partitions, entries in Ramanujan’s notebooks,...

We continue to explore the conjectural expressions of the Gromov-Witten potentials for a class of elliptically and K3 fibered Calabi-Yau 3-folds in the limit where the base P of the K3 fibration becomes infinitely large. At least in this limit we argue that the string partition function (= the exponential generating function of the Gromov-Witten potentials) can be expressed as an infinite produ...

We give an introduction to the theory of Borcherds products and to some number theoretic and geometric applications. In particular, we discuss how the theory can be used to study the geometry of Hilbert modular surfaces.

In different fields in space researches, Scientists are in need to deal with the product of matrices. In this paper, we develop conditions under which a product  of matrices chosen from a possibly infinite set of matrices 0 i i P    , j  M P j J     k i P   0 k k i  converges. There exists a vector norm such that all matrices in M are no expansive with respect to this norm and also ...

We classify the sequences 〈Sn | n ∈ N〉 of finite simple nonabelian groups such that ∏ n Sn has uncountable cofinality.