In this paper, we consider a class of connected oriented (with respect to Z/p) closed G-manifolds with a non-empty finite fixed point set, each of which is G-equivariantly formal, where G = Z/p and p is an odd prime. Using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a G-manifold in terms of algebra. This makes ...

We define a new notion of cuspidality for representations of GLn over a finite quotient ok of the ring of integers o of a non-Archimedean local field F using geometric and infinitesimal induction functors, which involve automorphism groups Gλ of torsion o-modules. When n is a prime, we show that this notion of cuspidality is equivalent to strong cuspidality, which arises in the construction of ...

In the present paper we start the systematic explicit construction of invariant differential operators by giving explicit description of one of the main ingredients the cuspidal parabolic subalgebras. We explicate also the maximal parabolic subalgebras, since these are also important even when they are not cuspidal. Our approach is easily generalised to the supersymmetric and quantum group sett...

The aim of this paper is to compute a simplicial cohomology group of some specific digital images. Then we define ringand algebra structures of a digital cohomology with the cup product. Finally, we prove a special case of the Borsuk-Ulam theorem fordigital images.

This paper is concerned with the relation between local cohomology modules defined by a pair of ideals and the Serre subcategories of the category of modules. We characterize the membership of local cohomology modules in a certain Serre subcategory from lower range or upper range.

For singular metrics, Ray and Singer’s analytic torsion formalism cannot be applied. Hence we do not have the so-called Quillen metric on determinant of cohomology with respect to a singular metric. In this paper, we introduce a new metric on determinant of cohomology by adapting a totally different approach. More precisely, by strengthening results in the first paper of this series, we develop...

The irreducible characters of a finite reductive group are partitioned into Harish-Chandra series that labelled by cuspidal pairs. In this note, we describe how one can algorithmically calculate those pairs using results Lusztig.

certain algebraic invariants of the integral group ring zg of a group g were introduced and investigated in relation to the problem of extending the farrell-tate cohomology, which is defined for the class of groups of finite virtual cohomological dimension. it turns out that the finiteness of these invariants of a group g implies the existence of a generalized farrell-tate cohomology for g whic...

In this paper, we will show how certain Hecke correspondences on modular curves may be characterized by their geometrical properties. We introduce the notion of a cuspidal correspondence and of an almost unramified correspondence (Definition 5) and prove (Theorem 1) that an irreducible almost unramified cuspidal correspondence on a modular curve is a modular correspondence. By considering the b...

We define a new notion of cuspidality for representations of GLn over a finite quotient ok of the ring of integers o of a non-Archimedean local field F using geometric and infinitesimal induction functors, which involve automorphism groups Gλ of torsion o-modules. When n is a prime, we show that this notion of cuspidality is equivalent to strong cuspidality, which arises in the construction of ...