The cohomology of period domains for reductive groups over finite fields
The Collineation Groups of Derived Translation Planes. II.
The Conjugating Representation of a Semisimple Group.
The Connes-Kasparov conjecture for almost connected groups and for linear -adic groups
Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C*-algebra of G is an isomorphism. The same is shown for the groups of k-rational points of any linear algebraic group over a local field k of characteristic zero.
The -property of linear and unitary groups.
The decomposition numbers of Hecke algebras of type F4 with unequal parameters.
The Decomposition numbers of the Hecke algebra of type F4.
The Decomposition of Tensors over Fields of Prime Characteristic.
The defect of weak approximation for homogeneous spaces
The density of representation degrees
For a group and a positive real number , define to be the number of integers less than which are dimensions of irreducible complex representations of . We study the asymptotics of for algebraic groups, arithmetic groups and finitely generated linear groups. In particular we prove an “alternative” for finitely generated linear groups in characteristic zero, showing that either there exists such that for all large , or is virtually abelian (in which case is bounded).
The dimension of some affine Deligne–Lusztig varieties
The Discrete Series of the Linear Groups SL (n, q).
The equations of conjugacy classes of nilpotent matrices.
The existence of equivariant pure free resolutions
Let be a polynomial ring in variables and let be a strictly increasing sequence of integers. Boij and Söderberg conjectured the existence of graded -modules of finite length having pure free resolution of type in the sense that for the -th syzygy module of has generators only in degree .This paper provides a construction, in characteristic zero, of modules with this property that are also -equivariant. Moreover, the construction works over rings of the form where is a polynomial...
The Faithful Linear Representation of Least Degree of Sn and An over a Field of Characteristic 2.
The Farrell cohomology of .
The First Cohomology Group of a Line Bundle on G/B.
The Fixed Point Subvarieties of Unipotent Transformations on Generalized Flag Varieties and the Green Functions. Combinatorial and Cohomological Treatments Centering GLn.
The Functional Equation. (Short Communication).
The fundamental theorem of prehomogeneous vector spaces modulo (With an appendix by F. Sato)
For a number field with ring of integers , we prove an analogue over finite rings of the form of the fundamental theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where is a big enough prime ideal of and . In the appendix, F.Sato gives an application of the Theorems 1.1, 1.3 and the Theorems A, B, C in J.Denef and A.Gyoja [Character sums associated to prehomogeneous vector spaces, Compos. Math., 113(1998), 237–346] to the functional equation of -functions...