Harish-Chandra vertices.
Heisenberg algebra and a graphical calculus
A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of the Heisenberg algebra in infinitely many variables. We construct bases of the vector spaces of morphisms between products of generating objects in this category.
Helices on some Fano threefolds : constructivity of semiorthogonal bases of
Invariants of several matrices.
- and -theory of the semi-direct product of the discrete 3-dimensional Heisenberg group by .
-theory of virtually poly-surface groups.
Ko for nonunital rings and Morita invariance.
Mackey functors on compact closed categories.
Modular representations of finite groups with trivial restriction to Sylow subgroups
Let be a field of characteristic . Let be a finite group of order divisible by and a -Sylow subgroup of . We describe the kernel of the restriction homomorphism , for the group of endotrivial representations. Our description involves functions that we call weak -homomorphisms. These are generalizations to possibly non-normal of the classical homomorphisms appearing in the normal case.
On existing of filtered multiplicative bases in group algebras.
On finite subgroups of groups of type VF.
On some invariants preserved by isomorphisms of tables of marks.
On the decomposition map of Grothendieck groups.
On the domain of the assembly map in algebraic -theory.
On the exponent of the cokernel of the forget-control map on K₀-groups
For groups that satisfy the Isomorphism Conjecture in lower K-theory, we show that the cokernel of the forget-control K₀-groups is composed by the NK₀-groups of the finite subgroups. Using this information, we can calculate the exponent of each element in the cokernel in terms of the torsion of the group.
On the leading terms of zeta isomorphisms and -adic -functions in non-commutative Iwasawa theory.
On the nonexistence of certain morphisms from Grassmannian to Grassmannian in characteristic 0.
On the values of equivariant zeta functions of curves over finite fields.
p-Nilpotence, classifying space indecomposability, and other properties of almost all finite groups.
Quasigroup automorphisms and symmetric group characters
The automorphisms of a quasigroup or Latin square are permutations of the set of entries of the square, and thus belong to conjugacy classes in symmetric groups. These conjugacy classes may be recognized as being annihilated by symmetric group class functions that belong to a -ideal of the special -ring of symmetric group class functions.