Invariants of several matrices.
Invariants of the half-liberated orthogonal group
The half-liberated orthogonal group appears as intermediate quantum group between the orthogonal group , and its free version . We discuss here its basic algebraic properties, and we classify its irreducible representations. The classification of representations is done by using a certain twisting-type relation between and , a non abelian discrete group playing the role of weight lattice, and a number of methods inspired from the theory of Lie algebras. We use these results for showing that...
Invariants, torsion indices and oriented cohomology of complete flags
Let be a split semisimple linear algebraic group over a field and let be a split maximal torus of . Let be an oriented cohomology (algebraic cobordism, connective -theory, Chow groups, Grothendieck’s , etc.) with formal group law . We construct a ring from and the characters of , that we call a formal group ring, and we define a characteristic ring morphism from this formal group ring to where is the variety of Borel subgroups of . Our main result says that when the torsion index...
Involutions and trace forms on exterior powers of a central simple algebra.
Irreducibilty of alternating and symmetric squares.
Irreducible characters of a Sylow p-subgroup of the orthogonal group.
Irreducible linear group-subgroup pairs with the same invariants.
Irreducible Representations of Finite Classical Groups.
Irreducible representations of quantum matrices.
Isocrystals with additional structure
Isométrics parfaites entre blocs de groupes linéaires ou unitaires.
Isomorphic Chevalley groups over integral domains
Isomorphisms in the Farrell cohomology of .
-invariant of linear algebraic groups
Let be a semisimple linear algebraic group of inner type over a field , and let be a projective homogeneous -variety such that splits over the function field of . We introduce the -invariant of which characterizes the motivic behavior of , and generalizes the -invariant defined by A. Vishik in the context of quadratic forms. We use this -invariant to provide motivic decompositions of all generically split projective homogeneous -varieties, e.g. Severi-Brauer varieties, Pfister quadrics,...
Jacquet functors and unrefined minimal K-types.
Jantzen's Filtrations of Weyl Modules.
-theory and stable algebra
Kac-Moody groups, hovels and Littelmann paths
We give the definition of a kind of building for a symmetrizable Kac-Moody group over a field endowed with a discrete valuation and with a residue field containing . Due to the lack of some important property of buildings, we call it a hovel. Nevertheless, some good ones remain, for example, the existence of retractions with center a sector-germ. This enables us to generalize many results proved in the semisimple case by S. Gaussent and P. Littelmann. In particular, if , the geodesic segments...
Kazhdan constants for SL (3, Z).
Kazhdan–Lusztig basis and a geometric filtration of an affine Hecke algebra, II
An affine Hecke algebras can be realized as an equivariant -group of the corresponding Steinberg variety. This gives rise naturally to some two-sided ideals of the affine Hecke algebra by means of the closures of nilpotent orbits of the corresponding Lie algebra. In this paper we will show that the two-sided ideals are in fact the two-sided ideals of the affine Hecke algebra defined through two-sided cells of the corresponding affine Weyl group after the two-sided ideals are tensored by . This...