Related papers: On Frobenius-Schur exponent bounds

In this paper, we obtain two analogues of the Sturm bound for modular forms in the function field setting. In the case of mixed characteristic, we prove that any harmonic cochain is uniquely determined by an explicit finite number of its…

We give a short proof for an explicit upper bound on the proportion of permutations of a given prime order $p$, acting on a finite set of given size $n$, which is sharp for certain $n$ and $p$. Namely, we prove that if $n\equiv k\pmod{p}$…

This thesis contains results relevant for two different classes of conformal field theory. We partly treat rational conformal field theory, but also derive results that aim at a better understanding of logarithmic conformal field theory.…

Let $R$ be a commutative noetherian ring. Denote by $\operatorname{mod} R$ the category of finitely generated $R$-modules and by $\operatorname{D^b}(R)$ the bounded derived category of $\operatorname{mod} R$. In this paper, we first…

We discuss the fermionization of fusion category symmetries in two-dimensional topological quantum field theories (TQFTs). When the symmetry of a bosonic TQFT is described by the representation category $\mathrm{Rep}(H)$ of a semisimple…

We construct a faithful categorical representation of an infinite Temperley-Lieb algebra on the periplectic analogue of Deligne's category. We use the corresponding combinatorics to classify thick tensor ideals in this periplectic Deligne…

We show that cubulated hyperbolic groups with spherical boundary of dimension 3 or at least 5 are virtually fundamental groups of closed, orientable, aspherical manifolds, provided that there are sufficiently many quasi-convex,…

Kaplansky conjectured that if H is a finite-dimensional semisimple Hopf algebra over an algebraically closed field k of characteristic 0, then H is of Frobenius type (i.e. if V is an irreducible representation of H then dimV divides dimH).…

We prove tight H\"olderian error bounds for all $p$-cones. Surprisingly, the exponents differ in several ways from those that have been previously conjectured; moreover, they illuminate $p$-cones as a curious example of a class of objects…

We study the category of finite--dimensional representations for a basic classical Lie superalgebra $\Lg=\Lg_0\oplus \Lg_1$. For the ortho--symplectic Lie superalgebra $\Lg=\mathfrak{osp}(1,2n)$ we show that certain objects in that category…

The main result is that the category of ordinary modules of an affine vertex operator algebra of a simply laced Lie algebra at admissible level is rigid and thus a braided fusion category. If the level satisfies a certain coprime property…

This paper classifies all modular data of integral modular fusion categories up to rank 13. Furthermore, it also classifies all integral half-Frobenius fusion rings up to rank 12. We find that each perfect integral modular fusion category…

Motivated by questions about $\mathbb{C}_p$-valued Fourier transform on the locally compact group $(\mathbb{Q}_p^d,+)$, we study invariant norms on the $p$-adic Schr\"odinger representation of the Heisenberg group. Our main result is a…

Let $p$ be a prime number. We compute the trivial source character tables of finite Frobenius groups $G$ with an abelian Frobenius complement $H$ and an elementary abelian Frobenius kernel of order $p^2$. More precisely, we deal with all…

Let I denote an R_+ -primary homogeneous ideal in a normal standard-graded Cohen-Macaulay domain over a field of positive characteristic p. We give a linear degree bound for the Frobenius powers I^[q] of I, q=p^e, in terms of the minimal…

In the paper we obtain some new upper bounds for exponential sums over multiplicative subgroups G of F^*_p having sizes in the range [p^{c_1}, p^{c_2}], where c_1,c_2 are some absolute constants close to 1/2. As an application we prove that…

Using the representation theory of the subgroups SL_2(Z_p) of the modular group we investigate the induced fusion algebras in some simple examples. Only some of these representations lead to 'good' fusion algebras. Furthermore, the…

We show that a compact rigid balanced braided monoidal category with enough compact projective objects gives rise to a system of mapping class group representations compatible with the gluing along marked intervals. A motivation to consider…

We consider selfinjective Artin algebras whose cohomology groups are finitely generated over a central ring of cohomology operators. For such an algebra, we show that the representation dimension is strictly greater than the maximal…

We develop the theory of Hopf bimodules for a finite rigid tensor category C. Then we use this theory to define a distinguished invertible object D of C and an isomorphism of tensor functors ?^{**} and D tensor ^{**}? tensor D^{-1}. This…