We construct a nonuniform lattice and an infinite family of uniform lattices in the automorphism group of a hyperbolic building with all links a fixed finite building of rank 2 associated to a Chevalley group. We use complexes of groups and basic facts about spherical buildings.

An infinite simple K∗-group of finite Morley rank of even type is a Chevalley group over an algebraically closed field of characteristic 2. Proposed draft. The supporting results are not complete at this time. For the current status, see the appendix.

We establish property (T) for a large class of groups graded by root systems, including elementary Chevalley groups and Steinberg groups of rank at least 2 over finitely generated commutative rings with 1. We also construct a group with property (T) which surjects onto all finite simple groups of Lie type and rank at least two.

We prove a Chevalley formula for the equivariant quantum multiplication of two Schubert classes in the homogeneous variety X = G/P . As in the case when X is a Grassmannian ([Mi1]), this formula implies an algorithm to compute the structure constants of the equivariant quantum cohomology algebra of X.

We define certain extensions of affine Weyl groups (distinct from these considered by K. Saito [S1] in the theory of extended affine root systems), prove an analogue of Chevalley theorem for their invariants, and construct a Frobenius structure on their orbit spaces. This produces solutions F (t1, . . . , tn) of WDVV equations of associativity polynomial in t1, . . . , tn−1, exp tn.

Let R be a commutative semilocal ring, G = SL(n; R) be the special linear group of degree n 3 over R and T = SD(n; R) be its subgroup of diagonal matrices. In the present paper we describe subgroups of G containing T under some mild restrictions on the residue elds of R. More precisely we prove the following result (we refer to Sections 2 o and 3 o for an explanation of all deenitions and notat...

has cardinality r ≥ 1. Let G be the F-rational points of a simple Chevalley group defined over F. In his thesis, Matsumoto [5] gave a beautiful construction for the metaplectic cover G̃ of G, a central extension of G by μr(F) whose existence is intimately connected with the deep properties of the r-th order Hilbert symbol (·, ·)F : F × × F → μr(F). Metaplectic groups figure prominently in the st...

We deene two (n + 1) graded Lie brackets on spaces of multilinear mappings. The rst one is able to recognize n-graded as-sociative algebras and their modules and gives immediately the correct diierential for Hochschild cohomology. The second one recognizes n-graded Lie algebra structures and their modules and gives rise to the notion of Chevalley cohomology.

We show that the two cuspidal unipotent characters of a finite Chevalley group E7(q) have Schur index 2, provided that q is an even power of a (sufficiently large) prime number p such that p ≡ 1 mod 4. The proof uses a refinement of Kawanaka’s generalized Gelfand–Graev representations and some explicit computations with the CHEVIE computer algebra system.

In a categorification of tensor products of fundamental representations of quantum sl(k) via highest weight categories, the indecomposable tilting modules descend to the canonical basis. Projective functors map tilting modules to tilting modules implying the coefficients of the canonical basis of tensor products of finite dimensional, irreducible representations under the action of the Chevalle...