In this paper the N = 4 D = 0 super Yang-Mills partition function is discussed for the case of arbitrary simple gauge group. It is explicitly evaluated in the case of orthogonal and symplectic groups with rank 4 6 N 6 11 and also for the exceptional groups F4, E6 in addition to known results. Also we suggest the answer for the case of SO(2N + 1),Sp(2N),SO(2N) groups for all N ∈ N. In addition, ...

let $g$ be a group and $pi(g)$ be the set of primes $p$ such that $g$ contains an element of order $p$. let $nse(g)$ be the set of the number of elements of the same order in $g$. in this paper, we prove that the simple group $l_2(p^2)$ is uniquely determined by $nse(l_2(p^2))$, where $pin{11,13}$‎.‎

This note is devoted to a more detailed description of one of the five simple exceptional Lie superalgebras of vector fields, cvect(0|3)∗, a subalgebra of vect(4|3). We derive differential equations for its elements, and solve these equations. Hence we get an exact form for the elements of cvect(0|3)∗. Moreover we realize cvect(0|3)∗ by ”glued” pairs of generating functions on a (3|3)-dimension...

The classical Tits construction of the exceptional simple Lie algebras has been extended in a couple of directions by using either Jordan superalgebras or composition superalgebras. These extensions are reviewed here. The outcome has been the discovery of some new simple modular Lie superalgebras.

In fact, this group is Spin(3), the 2-fold cover of SO(3), the group of rotations of R. This has been known for quite some time and is perhaps the simplest realization of Hamilton’s expectations about the potential of quaternions for physics. One reason for the renewed interest is the fact that the resulting substitution of matrices by quaternions speeds up considerably the numerical calculatio...

This paper begins the project of defining Arthur packets all unipotent representations for p-adic exceptional group G2. Here we treat most interesting case by and computing with component S3. We also show that distributions attached to these are stable, subject a hypothesis. is done using self-contained microlocal analysis simple equivariant perverse sheaves on moduli space homogeneous cubics i...