Related papers: Real blocks with dihedral defect groups revisited

Using combinatorics and character theory, we determine the imprimitive faithful complex characters, i.e., the irreducible faithful complex characters which are induced from proper subgroups, of the Schur covers of the symmetric and…

The purpose of this paper is to investigate the finite Frobenius groups with "perfect order classes"; that is, those for which the number of elements of each order is a divisor of the order of the group. If a finite Frobenius group has…

Let $G$ be a finite group of order divisible by two distinct primes $p$ and $q$. We show that $G$ possesses a non-trivial irreducible character of degree not divisible by $p$ nor $q$ lying in both the principal $p$- and $q$-block whenever…

Computations of Miller and Scheinerman suggest that the vast majority of the zeros appearing in the character table of the symmetric group are of a certain special type. While we cannot prove this, we resolve a conjecture arising in their…

We construct blocks of finite groups with arbitrarily large $\mathcal{O}$-Morita Frobenius numbers. There are no known examples of two blocks defined over $\mathcal{O}$ that are not Morita equivalent but the corresponding blocks defined…

Mason and Ng have given a generalization to semisimple quasi-Hopf algebras of Linchenko and Montgomery's generalization to semisimple Hopf algebras of the classical Frobenius-Schur theorem for group representations. We give a simplified…

In this note, we construct bipartite 2-walk-regular graphs with exactly 6 distinct eigenvalues as incidence graphs of group-divisible designs with the dual property. For many of them, we show that they are 2-arc-transitive dihedrants. We…

Eaton and Moret\'o proposed an extension of Brauer's famous height zero conjecture on blocks of finite groups to the case of non-abelian defect groups, which predicts the smallest non-zero height in such blocks in terms of local data. We…

In this article, we study $2$-designs with $\lambda=2$ admitting a flag-transitive almost simple automorphism group with socle a finite simple exceptional group of Lie type, and we prove that such a $2$-design does not exist. In conclusion,…

We investigate the rigidity and asymptotic properties of quantum SU(2) representations of mapping class groups. In the spherical braid group case the trivial representation is not isolated in the family of quantum SU(2) representations. In…

This paper shows how internal models for polymorphic lambda calculi arise in any 2-category with a notion of discreteness. We generalise to a 2-categorical setting the famous theorem of Peter Freyd saying that there are no sufficiently…

In this note we classify two-dimensional continued fractions for cubic irrationalities constructed by matrices with not large norm ($|*| \le 6$). The classification is based on the following new result: the class of matrices with an…

We consider the degree-diameter problem for Cayley graphs of dihedral groups. We find upper and lower bounds on the maximum number of vertices of such a graph with diameter 2 and degree $d$. We completely determine the asymptotic behaviour…

We show that, with the exception of the words $a^2ba^2$ and $b^2ab^2$, all (finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can actually be found in that sequence as segments (up to exchange of letters in the infinite…

In this paper, we propose a new approach towards the classification of spherical fusion categories by their Frobenius-Schur exponents. We classify spherical fusion categories of Frobenius-Schur exponent 2 up to monoidal equivalence. We also…

In this paper, we prove that a \(p\)-block with abelian defect group is inertial if it covers a \(p\)-block of a normal subgroup of \(p\)-power index having only one irreducible Brauer character orbit.

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…

In this paper we explicitly determine all indicators for the Drinfel'd doubles of the symmetric group acting upon up to 10 objects. We explore when distinct characters give exactly the same indicators and when the indicators have a zero…

We prove the existence of cluster characters for Hom-infinite cluster categories. For this purpose, we introduce a suitable mutation-invariant subcategory of the cluster category. We sketch how to apply our results in order to categorify…

Let $G = {\rm U}(2m, {\mathbb F}_{q^2})$ be the finite unitary group, with $q$ the power of an odd prime $p$. We prove that the number of irreducible complex characters of $G$ with degree not divisible by $p$ and with Frobenius-Schur…