Cohomology of Chevalley groups over finite fields

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.

Heisenberg groups over finite fields

ing this computation, for given k-vectorspace V with non-degenerate alternating form 〈, 〉, put a Lie algebra [2] structure h on V ⊕ k by Lie bracket [v ⊕ z, v′ ⊕ z′] = 0⊕ 〈v, v′〉 In exponential coordinates on H, the exponential map h→ H with H ≈ V ⊕ k is notated exp(v ⊕ z) = v ⊕ z with Lie group structure on H by (v ⊕ z) · (v′ ⊕ z′) = (v + v′)⊕ (z + z′ + 〈v, v ′〉 2 ) (exponential coordinates in...

Chevalley Groups over Commutative Rings

Characters of unipotent groups over finite fields

Let G be a connected unipotent group over a finite field Fq. In this article we propose a definition of L-packets of complex irreducible representations of the finite group G(Fq) and give an explicit description of L-packets in terms of the so-called “admissible pairs” for G. We then apply our results to show that if the centralizer of every geometric point of G is connected, then the dimension...

Characters of Reductive Groups over Finite Fields

Let E be a connected reductive algebraic group over C and let W be its Weyl group. The Springer correspondence allows us to parametrize the irreducible representations E of W as F = F^^ where u is a unipotent element in G (up to conjugacy) and <p is an irreducible representation of the group of components AH(u) = ZH(u)IZ°H(u). (However, not all <p arise in the parametrization.) For F = F^Uttp) ...