相关论文: Tannakian reconstruction of reductive group scheme…
A Tannakian category is an abelian tensor category equipped with a fiber functor and additional structures which ensure that it is equivalent to the category of representations of some affine groupoid scheme acting on the spectrum of a…
We apply analytic perturbation theory in next-to-next-to-leading order to inclusive semileptonic $\tau$-decay and study the renormalization scheme dependence. We argue that the renormalization scheme ambiguity is considerably reduced in the…
The reduction of nonholonomic systems is formulated in terms of Dirac reduction. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in detail.
Scheme independence of exact renormalization group equations, including independence of the choice of cutoff function, is shown to follow from general field redefinitions, which remains an inherent redundancy in quantum field theories.…
This paper establishes Noether's classical degree bound $\beta(G) \le |G|$ for finite and linearly reductive group schemes. On the other hand, we provide examples of infinitesimal group schemes where $\beta(G)$ is unbounded. We also…
The irreducible bases in the icosahedral group space are calculated explicitly by reducing the regular representation. The symmetry adapted bases of the system with {\bf I} or {\bf I}$_{h}$ symmetry can be calculated easily and generally by…
We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of…
Let $k$ be a nonperfect separably closed field. Let $G$ be a (possibly non-connected) reductive group defined over $k$. We study rationality problems for Serre's notion of complete reducibility of subgroups of $G$. In our previous work, we…
Let k be an algebraically closed field. Given an extension A : B of finite-dimensional k- algebras, we establish criteria ensuring that the representation-theoretic notion of polynomial growth is preserved under ascent and descent. These…
We study analogues for the Tate-Shafarevich group for Abelian schemes with everywhere good reduction over higher dimensional bases over finite fields.
We prove that separable extensions of noetherian rings and finite \'etale morphisms of noetherian schemes give rise to separable extensions of singularity categories.
A natural question in the theory of Tannakian categories is: What if you don't remember $\Forget$? Working over an arbitrary commutative ring $R$, we prove that an answer to this question is given by the functor represented by the \'etale…
We construct quark mixing matrices within a group theoretic framework which is easily applicable to any number of generations. Familiar cases are retrieved and related, and it is hoped that our viewpoint may have advantages both…
We prove a $p$-nilpotency criterion for finite groups in terms of the element orders of its $p'$-reduced sections that extends a nilpotency criterion by T{\u{a}}rn{\u{a}}uceanu.
We incorporate metric data into the framework of Tannaka-Krein duality. Thus, for any group with left invariant metric, we produce a dual metric on its category of unitary representations. We characterize the conditions under which a…
The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…
In this paper, we study the combinatorics of congruence subgroups of the modular group by generalizing results obtained in the non-modular case. For this, we define a notion of irreducible solutions from which we can build all the…
The partial success of the block renormalization group techniques is analysed in terms of a functional operator which formalizes the idea of self-replicability of a system in terms of smaller blocks which are similar to the original. The…
The tame fundamental group scheme for an algebraic variety is the maximal linearly reductive quotient of Nori's fundamental group scheme. In this paper, we study the tame fundamental group schemes of smooth curves defined over algebraically…
We define an unstable equivariant motivic homotopy category for an algebraic group over a Noetherian base scheme. We show that equivariant algebraic $K$-theory is representable in the resulting homotopy category. Additionally, we establish…