Related papers: Groups of components and Weil restriction

For a group $G$ of not prime power order, Oliver showed that the obstruction for a finite CW-complex $F$ to be the fixed point set of a contractible finite $G$-CW-complex is the Euler characteristic $\chi(F)$. He also has the similar…

In this note a combinatorial formula related to the symmetric group is generalized to an arbitrary finite Weyl group.

Reductions of N-wave type equations related to simple Lie algebras and the hierarchy of their Hamiltonian structures are studied. The reduction group G_R is realized as a subgroup of the Weyl group of the corresponding algebra. Some of the…

In this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions…

We obtain new bounds on short Weil sums over small multiplicative subgroups of prime finite fields which remain nontrivial in the range the classical Weil bound is already trivial. The method we use is a blend of techniques coming from…

Let A be a character sheaf on a reductive connected group G over an algebraically closed field. Assuming that the characteristic is not bad, we show that for certain conjugacy classes D in G the restriction of A to D is a local system up to…

We study a trace formula for tamely ramified abelian varieties $A$ over a complete discretely valued field, which expresses the Euler characteristic of the special fiber of the N\'eron model of $A$ in terms of the Galois action on the…

Let $A$ be an abelian variety over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by the Weil polynomial $f_A$. We assume that $f_A$ is separable. For a given prime number $\ell\neq\mathrm{char}\, k$ we give a…

In the spirit of an earlier result of M\"uller on the Heisenberg group we prove a restriction theorem on a certain class of two step nilpotent Lie groups. Our result extends that of M\"uller also in the framework of the Heisenberg group.

This note constitutes a brief survey of our recent work on the problem of determining, for a given real Lie group~$G$, the set of representations~$V$ in which the longest element~$w_0$ of the restricted Weyl group~$W$ acts nontrivially on…

Let (g,[p]) be a finite-dimensional restricted Lie algebra, defined over an algebraically closed field k of characteristic p>0. The scheme of tori of maximal dimension of g gives rise to a finite group S(g) that coincides with the Weyl…

Assume that two algebraic varieties of finite type over the complex numbers are related by a morphism whose fibers are precisely the orbits for the action of a unipotent group. We show that the two varieties have the same topological Euler…

Frame theory has been a popular subject in the design of structured signals and codes in recent years, with applications ranging from the design of measurement matrices in compressive sensing, to spherical codes for data compression and…

We show that tilting modules for quantum groups over local Noetherian domains exist and that the indecomposable tilting modules are parametrized by their highest weight. For this we introduce a model category ${\mathcal X}={\mathcal…

For a simple complex Lie algebra of finite rank and classical type, we fix a triangular decomposition and consider the simple Levi subalgebras associated to closed subsets of roots. We study the restriction of global and local Weyl modules…

For a discrete subgroup of an indefinite unitary group $U(1,n+1)$, $n\geq 1$, consider the attached modular variety. Using local Borcherds products, we study Heegner divisors in the local Picard group over a boundary component the…

We investigate amenability for $W^*$-Fell bundles over a discrete group $G$, with a focus on its characterization via approximation properties and conditional expectations. Building on the notion of $W^*$-amenability, we construct an…

In this note, we present the theorem of extension of birational group laws in both settings of classical varieties (Weil) and schemes (Artin). We improve slightly the original proof with a more direct construction of the group extension and…

Let A = (A,V) be a complex hyperplane arrangement and let L(A) denote its intersection lattice. The arrangement A is called supersolvable, provided its lattice L(A) is supersolvable. For X in L(A), it is known that the restriction A^X is…

We find the irreducible decomposition of the Weil representation of the unitary group $\mathrm{U}_{2n}(A)$, where $A$ is a ramified quadratic extension of a finite, commutative, local, principal ideal ring $R$ and the nilpotency degree of…