相关论文: Collar lemma for Hitchin representations

We give a new proof of Lucas' Theorem in elementary number theory.

We prove the modular branching rule of the cyclotomic Hecke algebras, which has remained open.

This article presents an equivalent formulation of the implicit complementarity problem. We demonstrate that solution of the equivalent formulation is equivalent to the solution of the implicit complementarity problem. Moreover, we provide…

An analog of Picard's little theorem for entire functions of matrices is proved.

We compute the supports of the perverse cohomology sheaves of the Hitchin fibration for $GL_n$ over the locus of reduced spectral curves. In contrast to the case of meromorphic Higgs fields we find additional supports at the loci of…

We prove a formula conjectured by the third author expressing certain Hodge integrals in terms of certain Chern-Simons link invariants. Such invariants also arise in the representation theory of Kac-Moody algebras.

We prove an analogue of the Brody lemma in the framework of Riemannian manifolds. We also present new examples of Riemannian manifolds that are hyperbolic in the sense of Kobayashi.

We show the pointwise version of the Ste\v{c}kin theorem on approximation by de la Vall\'ee-Poussin means. The result on norm approximation is also derived.

We give an extension to a nonconvex setting of the classical radial representation result for lower semicontinuous envelope of a convex function on the boundary of its effective domain. We introduce the concept of radial uniform upper…

The converse of Fortin's Lemma in Banach spaces is established in this Note.

An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…

The object of this work is to present the status of art of an open problem: to provide an analogue for Shimura curves of the Ihara's lemma \cite{Ihara73} which holds for modular curves. We will describe our direct result towards the…

We observe that Whitehead's lemma is an immediate consequence of Stallings folds.

Some congruence relations satisfied by the theta series associated with the Leech lattice are given.

In this paper, we introduce the concepts of representation and dual representation for averaging Leibniz algebras. We also develop a cohomology theory for these algebras. Additionally, we explore the infinitesimal and formal deformation…

For any genus g > 1 we give an example of a family of smooth complex projective curves of genus g such that the image of the monodromy representation of the Hitchin connection on the sheaf of generalized SL(2)-theta functions of level l…

We prove an injective version of Schanuel's lemma from homological algebra in the setting of exact categories.

For general non-classical systems, we study the different classical representations that fulfill the specific context dependence imposed by the hidden measurement system formalism introduced in quant-ph/0008061. We show that the collection…

The Hilbert symbol $(\cdot,\cdot )$ from characteristic $\neq 2$ has two analogues in characteristic $2$, $[\cdot,\cdot )$ and $((\cdot,\cdot ))$. In characteristic $\neq 2$ we have a well known result called the common slot lemma or the…

We study the hyperk\"ahler analogues of moduli spaces of semistable n-gons in complex projective space. We prove that the hyperk\"ahler Kirwan map is surjective and produce a formula that recursively calculates the Betti numbers of these…