Related papers: A note about the (2,3)-generation of SL_12(q)

In this paper we give explicit (2,3)-generators of the unitary groups SU_6(q^ 2), for all q. They fit into a uniform sequence of likely (2,3)-generators for all n>= 6.

We prove that the groups PSL_n(q) are (2,3)-generated for n=9,10 or 11 and all q. Actually, we find out explicit generators x_n and y_n of respective orders 2 and 3, for the groups SL_n(q).

We complete the classification of the finite special linear groups $\SL_n(q)$ which are $(2,3)$-generated, i.e., which are generated by an involution and an element of order $3$. This also gives the classification of the finite simple…

The complete classification of the finite simple groups that are $(2,3)$-generated is a problem which is still open only for orthogonal groups. Here, we construct $(2, 3)$-generators for the finite odd-dimensional orthogonal groups…

In this paper we prove that the unitary groups $SU_n(q^2)$ are $(2,3)$-generated for any prime power $q$ and any integer $n\geq 8$. By previous results this implies that, if $n\geq 3$, the groups $SU_n(q^2)$ and $PSU_n(q^2)$ are…

We construct $(2,3)$-generators for the finite $8$-dimensional orthogonal groups, proving the following results: the groups $\Omega_8^+(q)$ and $P\Omega_8^+(q)$ are $(2,3)$-generated if and only if $q\geq 4$; the groups $\Omega_8^-(q)$ and…

We compute the characters of real irreducible representations of SL(2,q), the special linear group on q letters, for an odd prime $q$. Moreover, we give the dimensions of these irreducible representations under the actions of cyclic…

In this paper we study the (2,k)-generation of the finite classical groups SL(4,q), Sp(4,q), SU(4,q^2) and their projective images. Here k is the order of an arbitrary element of SL(2,q), subject to the necessary condition k>= 3. When q is…

In this paper we determine the classical simple groups of dimension r=3,5 which are (2,3)-generated (the cases r = 2, 4 are known). If r = 3, they are PSL_3(q), q <> 4, and PSU_3(q^2), q^2 <> 9, 25. If r = 5 they are PSL_5(q), for all q,…

The quantum group SL_q(2,R) at roots of unity is introduced by means of duality pairings with the quantum algebra U_q(sl(2,R)). Its irreducible representations are constructed through the universal T-matrix. An invariant integral on this…

This paper is a new important step towards the complete classification of the finite simple groups which are $(2, 3)$-generated. In fact, we prove that the symplectic groups $Sp_{2n}(q)$ are $(2,3)$-generated for all $n\geq 4$. Because of…

Let SL(2,q) be the group of 2X2 matrices with determinant one over a finite field F of size q. We prove that if q is even, then the product of any two noncentral conjugacy classes of SL(2,q) is the union of at least q-1 distinct conjugacy…

$\operatorname{SL}(2,q)$-unitals are unitals of order $q$ admitting a regular action of $\operatorname{SL}(2,q)$ on the complement of some block. We introduce three non-classical affine $\operatorname{SL}(2,8)$-unitals and their full…

We give a complete list of orbifolds uniformised by discrete non-elementary two-generator subgroups of PSL(2,C) without invariant plane whose generators and their commutator have real traces.

We present an efficient method for computing the ${\rm SL}(3,\mathbb{C})$-character varieties of two-generator groups.

$\operatorname{SL}(2,q)$-unitals are unitals of order $q$ admitting a regular action of $\operatorname{SL}(2,q)$ on the complement of some block. They can be obtained from affine $\operatorname{SL}(2,q)$-unitals via parallelisms. We compute…

The spectrum of $L^2$ on a pseudo-unitary group $U(p,q)$ (we assume $p\ge q$ naturally splits into $q+1$ types. We write explicitly orthogonal projectors in $L^2$ to subspaces with uniform spectra (this is an old question formulated by…

In this paper we prove that the finite simple groups $PSp_6(q)$, $\Omega_7(q)$ and $PSU_7(q^2)$ are (2,3)-generated for all q. In particular, this result completes the classification of the (2,3)-generated finite classical simple groups up…

Let $G$ be a finite almost simple group. It is well known that $G$ can be generated by 3 elements, and in previous work we showed that 6 generators suffice for all maximal subgroups of $G$. In this paper we consider subgroups at the next…

We give a construction of sl_2-categorifications (in the sense of Chuang-Rouquier) for representations of U_q(gl_n), for generic q and for q a root of unity.