Related papers: Infinite characters of type II on $SL_n(\mathbb{Z}…

Answering a question of J. Rosenberg, we construct the first examples of infinite characters on $GL_n(\mathbf{K})$ for a global field $\mathbf{K}$ and $n\geq 2.$ The case $n=2$ is deduced from the following more general result. Let $G$ a…

We construct infinite cubefree binary words containing exponentially many distinct squares of length n. We also show that for every positive integer n, there is a cubefree binary square of length 2n.

We give methods for constructing many self-dual $\mathbb{Z}_m$-codes and Type II $\mathbb{Z}_{2k}$-codes of length $2n$ starting from a given self-dual $\mathbb{Z}_m$-code and Type II $\mathbb{Z}_{2k}$-code of length $2n$, respectively. As…

We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2,2,2) whose Hilbert 2-class fields are finite.

We determine the indecomposable characters of several classes of infinite dimensional groups associated with operator algebras, including the unitary groups of arbitrary unital simple AF algebras and II$_1$ factors.

In this paper, we show that an extremal Type II $\ZZ_{2k}$-code of length $n$ dose not exist for all sufficiently large $n$ when $k=2,3,4,5,6$.

We give several formulas for the character of an arbitrary irreducible finite--dimensional representation for the Yangian of sl_2.

We show that for any knot there exist only finitely many irreducible metabelian characters in the $SL(2,\mathbb{C})$-character variety of the knot group, and the number is given explicitly by using the determinant of the knot. Then it turns…

We demonstrate that there are infinitely many integers that cannot be expressed as the sum of two squares of integers and up to two non-negative integer powers of 2.

We prove identities for six infinite series whose values involve linear combinations of $\pi$ and $\operatorname{ln} 2$, that do not appear in standard infinite series references.

In this note, we demonstrate that every binary doubly even self-dual code of length $40$ can be realized as the residue code of some extremal Type II $\mathbb{Z}_4$-code. As a consequence, it is shown that there are at least $94356$…

We characterize the squares occurring in infinite overlap-free binary words and construct various alpha power-free binary words containing infinitely many overlaps.

In this article we construct examples of L-indistinguishable overconvergent eigenforms for an inner form of SL(2).

For lengths 8,16 and 24, it is known that there is an extremal Type II Z2k-code for every positive integer k. In this paper, we show that there is an extremal Type II Z2k-code of lengths 32,40,48,56 and 64 for every positive integer k. For…

It has been shown recently that the toroidally compactified type IIB string effective action possesses an SL(2, R) invariance. Using this symmetry we construct an infinite family of macroscopic string-like solutions permuted by SL(2, Z)…

We determine the characters of SL(2) representations of groups and surface groups.

In this article, we count the number of return words in some infinite words with complexity 2n+1. We also consider some infinite words given by codings of rotation and interval exchange transformations on k intervals. We prove that the…

We give closed formulas for all vectors of the canonical basis of a level 2 irreducible integrable representation of $U_v(sl_\infty)$. These formulas coincide at v=1 with Lusztig's formulas for the constructible characters of the…

In this paper we study characters on special linear groups SL_n(R), where R is either an infinite field or the localization of an order in a number field. We give several applications to the theory of measure preserving actions,…

We prove that the Lie algebra $\mathfrak{sl}_n(\textbf{F}_q)$ of traceless matrices over a finite field of characteristic $p$ can be generated by $2$ elements with exceptions when $(n, p)$ is $(3, 3)$ or $(4,2)$. In the latter cases, we…