Related papers: Odd Character Degrees for Sp(2n,2)

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…

We restrict the possibilities for the character degrees of $p$-groups $G$ satisfying $|G:G'| = p^2$. E.g. if $G$ is of maximal class and has an irreducible character of degree $> p$, then it has such a character of degree at most…

We prove that the inductive AM condition introduced by Britta Sp\"ath is true for the simple alternating groups in characteristic 2. To achieve this we give an equivalent of a well known result on blocks of the symmetric groups with the…

We present a bialternant formula for odd symplectic characters, which are the characters of indecomposable modules of odd symplectic groups introduced by R. Proctor. As an application, we give a linear algebraic proof to an odd symplectic…

By exploiting relationships between the values taken by ordinary characters of symmetric groups we prove two theorems in the modular representation theory of the symmetric group. 1. The decomposition matrices of symmetric groups in odd…

Let p be an odd prime, and A_n the alternating group of degree n. We determine which ordinary irreducible representations of A_n remain irreducible in characteristic p, verifying the author's conjecture from [Represent. Theory 14, 601-626].…

Let $F$ be a $p$-adic field of characteristic zero and odd residual characteristic. Let $\mathbf{Sp}_{2n}(F)$ denote the symplectic group defined over $F$, where $n\geq 2$. We prove that the Speh representations $\mathcal{U}(\delta,2)$,…

We complete the proof of the inductive Feit condition and the inductive Galois-McKay condition for the simple groups $\operatorname{PSL}_2(q)$. We also prove that the Suzuki groups $^{2}B_2(2^{2n+1})$ satisfy the inductive Feit condition.

We find explicit models for the PSL(2,C)- and SL(2,C)-character varieties of the fundamental groups of complements in S^3 of an infinite family of two-bridge knots that contains the twist knots. We compute the genus of the components of…

It is known that, if all the real-valued irreducible characters of a finite group have odd degree, then the group has normal Sylow $2$-subgroup. We generalize this result for Sylow $p$-subgroups, for any prime number $p$, while assuming the…

We will give the graded ring of Siegel modular forms of degree two with respect to a non-split symplectic group explicitly.

We consider II$_1$ factors $M$ which can be realized as inductive limits of subfactors, $N_n \nearrow M$, having spectral gap in $M$ and satisfying the bi-commutant condition $(N_n'\cap M)'\cap M=N_n$. Examples are the enveloping algebras…

We use intermediate symplectic characters to give a proof and variations of Hopkins' conjecture, now proved by Hopkins and Lai, on the number of shifted plane partitions of shifted double staircase shape with bounded entries. In fact, we…

We study the symplectic semi-characteristic of a closed 4n-dimensional symplectic manifold. First, using the even-degree part of the primitive cohomology, we define the symplectic semi-characteristic. Second, using a vector field with…

Motivated by the incidence problems between points and flats of a symplectic polar space, we study a large class of submodules of the space of functions on the standard module of a finite symplectic group of odd characteristic. Our…

We determine the non-abelian composition factors of the finite groups with Sylow normalizers of odd order. As a consequence, among others, we prove the McKay conjecture and the Alperin weight conjecture for these groups.

We classify bireflectional elements (products of 2 involutions) in symplectic groups Sp$(2n, K)$ over a field $K$. We also classify rev ersible elements (elements conjugate to their inverses) and bireflectional elements in finite projective…

A classical theorem of John Thompson on character degrees asserts that if the degree of every ordinary irreducible character of a finite group $G$ is 1 or divisible by a prime $p$, then $G$ has a normal $p$-complement. We obtain a…

The classification of irreducible, spherical characters of the infinite-dimensional unitary/orthogonal/symplectic groups can be obtained by finding all possible limits of normalized, irreducible characters of the corresponding…

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…