Related papers: Digit permutations revisited

We consider the group formed by finite renormalizations as an infinite-dimensional Lie group. It is demonstrated that for the finite renormalization of the gauge coupling constant its generators $\hat L_n$ with $n\ge 1$ satisfy the…

For every pair of positive integers $p > q$ we construct a one-relator group $R_{p,q}$ whose Dehn function is $\simeq n^{2 \alpha}$ where $\alpha = \log_2(2p / q)$. The group $R_{p,q}$ has no subgroup isomorphic to a Baumslag-Solitar group…

Our main result is elementary and concerns the relationship between the multiplicative groups of the coordinate and endomorphism rings of the formal additive group over a field of characteristic $p>0$. The proof involves the combinatorics…

In this note we consider a $p$-isometrisability property of discrete groups. If $p=2$ this property is equivalent to unitarisability. We prove that any group containing a non-abelian free subgroup is not $p$-isometrisable for any $p\in (1,…

We study irreducible spherical unitary representations of the Drinfeld double of a $q$-deformation of a connected simply connected compact Lie group, which can be considered as a quantum analogue of the complexification of the Lie group. In…

Let $A$ be an associative algebra over a field $F$ of characteristic zero and let $L$ be a Lie algebra over $F$. If $L$ acts on $A$ by derivations, then such an action determines an action of its universal enveloping algebra $U(L)$ and in…

Since the seminal work of Wan, Poonen, and Sheats in the 1990's, we have been searching for the correct general statement of the Riemann Hypothesis ("RH") which appears implicit in their results. Recently, upon viewing the extension $\C/\R$…

This survey article is an introduction to some of Lusztig's work on the character theory of a finite group of Lie type $G(F_q)$, where $q$ is a power of a prime~$p$. It is partly based on two series of lectures given at the Centre Bernoulli…

For a normal F-finite variety $X$ and a boundary divisor $\Delta$ we give a uniform description of an ideal which in characteristic zero yields the multiplier ideal, and in positive characteristic the test ideal of the pair $(X,\Delta)$.…

N. Katz has shown that any irreducible representation of the Galois group of F_q((t)) has unique extension to a special representation of the Galois group of k(t) unramified outside 0 and infinity and tamely ramified at infinity. In this…

This is an introduction to the author theory of cyclic p-extensions of an absolutely unramified complete discrete valuation field K with arbitrary residue field of characteristic p. In this theory a homomorphism is constructed from the…

We work out axioms for the duals $G\subset U_N^+$ of the finite quantum permutation groups, $F\subset S_N^+$ with $|F|<\infty$, and we discuss how the basic theory of such quantum permutation groups partly simplifies in the dual setting. We…

In the past few years, an action of $\mathrm{PGL}_2(\mathbb F_q)$ on the set of irreducible polynomials in $\mathbb F_q[x]$ has been introduced and many questions have been discussed, such as the characterization and number of invariant…

Let $n \ge 3$ be an integer. Let $P_n = \{1, 2, 3, ..., n-1, n \}$ and let $S_n$ be the symmetric group of permutations on $P_n$. Motivated by the theory of discrete dynamical systems on the interval, we associate each permutation $\si_n$…

In this paper, we investigate permutation polynomials over the finite field $\mathbb F_{q^n}$ with $q=2^m$, focusing on those in the form $\mathrm{Tr}(Ax^{q+1})+L(x)$, where $A\in\mathbb F_{q^n}^*$ and $L$ is a $2$-linear polynomial over…

We classify all non-degenerate skew-hermitian forms defined over certain local rings, not necessarily commutative, and study some of the fundamental properties of the associated unitary groups, including their orders when the ring in…

In this paper, we investigate abstract homomorphism from the special linear group over complete discrete valuation rings with finite residue field, such as the ring of p-adic integers, into the general linear group over the reals. We find…

We study isolated quotient singularities by finite and linearly reductive group schemes (lrq singularities for short) and show that they satisfy many, but not all, of the known properties of finite quotient singularities in characteristic…

If $K/\mathbb Q$ is a finite Galois extension with an almost monomial Galois group and if $s_0\in\mathbb C\setminus\{1\}$ is not a common zero for any two Artin L-functions associated to distinct complex irreducible characters of the Galois…

We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.