Involutions in Chevalley groups over fields of even order

Chevalley Groups over Commutative Rings

Lattices of minimum covolume in Chevalley groups over local fields of positive characteristic

In this article, we show that if G is a simply connected Chevalley group of either classical type of rank bigger than 1 or type E6, and q > 9 is a power of a prime number p > 5, then G = G(Fq((t))), up to an automorphism, has a unique lattice of minimum covolume, which is G(Fq[t]). 1

Infinite Dimensional Chevalley Groups and Kac-moody Groups over Z

Let A be a symmetrizable generalized Cartan matrix. Let g be the corresponding Kac-Moody algebra. Let G(R) be Tits’ Kac-Moody group functor over commutative rings R associated to g. Then G(R) is given by five axioms KMG1-KMG5 which are natural extensions of the properties of Chevalley-Demazure group schemes. We give a construction of the Tits functor for symmetrizable Kac-Moody groups G using i...

A semi-recursion for the number of involutions in special orthogonal groups over finite fields

Let I(n) be the number of involutions in a special orthogonal group SO(n,Fq) defined over a finite field with q elements, where q is the power of an odd prime. Then the numbers I(n) form a semi-recursion, in that for m > 1 we have I(2m+ 3) = (q + 1)I(2m+ 1) + q(q − 1)I(2m− 2). We give a purely combinatorial proof of this result, and we apply it to give a universal bound for the character degree...

Finite Fields, Root Systems and Orbit Numbers of Chevalley Groups

We describe combinatorial techniques to determine the numbers of semisim-ple conjugacy classes and adjoint orbits with xed class of centralizers for simply connected nite groups of Lie type.