相关论文: On bases of certain Grothendieck groups

We study the new basis of the (complexified) Grothendieck group of unipotent representations of a split reductive group over a finite field. For exceptional types we use a definition of the new basis which differs from the earlier one.

In previous papers the author introduced a new basis of the Grpthendieck group of unipotent representations of a finite Chevalley group. In type D the definition of this basis was stated without proof. In this paper we provide the missing…

In this paper we use families of finite subgroups to study Grothendieck rings associated to certain discrete groups, such as the arithmetic ones.

Let G(F_q) be the group of rational points of a simple algebraic group defined and split over a finite field F_q. In this paper we define a new basis for the Grothendieck group of unipotent representations of G(F_q).

We determine the irreducible constituents of the Steinberg character of an orthogonal group over a finite field restricted to the orthogonal group of one less dimension

A linear algebraic group G defined over a field k is called special if every G-torsor over every field extension of k is trivial. In 1958 Grothendieck classified special groups in the case where the base field is algebraically closed. In…

In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…

We compute the motive of the classifying stack of an orthogonal group in the Grothendieck ring of stacks over a field of characteristic different from two.

Differential-geometric structures on the space of orbits of a finite Coxeter group, determined by Groth\'endieck residues, are calculated. This gives a construction of a 2D topological field theory for an arbitrary Coxeter group.

For an isotropic reductive group G satisfying a suitable rank condition over an infinite field k, we show that the sections of the $\mathbb{A}^1$-fundamental group sheaf of G over an extension field L/k can be identified with the second…

In a recent paper I defined a new basis for the Grothendieck group of unipotent representations of an almost simple Chevalley group over a finite field. The definition for classical types was different from that for exceptional types. In…

We define the Grothendieck group of an n-angulated category and show that for odd n its properties are as in the special case of n=3, i.e. the triangulated case. In particular, its subgroups classify the dense and complete n-angulated…

We will calculate completely the Grothendieck rings, in the sense of first order logic, of o-minimal expansions of ordered abelian groups by introducing the notion of the bounded Euler characteristic.

We prove a version of Knebusch's Norm Principle for finite \'etale extensions of semi-local Noetherian domains with infinite residue fields of characteristic different from 2. As an application we prove Grothendieck's conjecture on…

Given an abelian variety over a field with a discrete valuation, Grothendieck defined a certain open normal subgroup of the absolute inertia group. This subgroup encodes information on the extensions over which the abelian variety acquires…

Grothendieck proposed a theory of regular polyhedra over finite fields in Section 4 of \textit{Esquisse d'un Programme}. He isolates certain key parameters from the automorphism groups of regular polyhedra, which can be extended to any…

We define the Grothendieck group of an $n$-exangulated category. For $n$ odd, we show that this group shares many properties with the Grothendieck group of an exact or a triangulated category. In particular, we classify dense complete…

We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.

We will give the graded ring of Siegel modular forms of degree two with respect to a non-split symplectic group explicitly.

In this article we give a concept of ground subgroup for finite and countable groups. By our definition such a subgroup of a group depends on a given subset of the group and on a given partition of the subset. For finite and free groups we…