Related papers: Deformed Harish-Chandra homomorphism for the cycli…
We prove the weight part of Serre's conjecture in generic situations for forms of $U(3)$ which are compact at infinity and split at places dividing $p$ as conjectured by Herzig. We also prove automorphy lifting theorems in dimension three.…
This paper is devoted to investigating the centre of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ via establishing the Harish-Chandra homomorphism. Based on the Rosso form and the representation theory of weight modules, we prove…
Let $G$ be a semisimple algebraic group over the complex numbers and $K$ be a connected reductive group mapping to $G$ so that the Lie algebra of $K$ gets identified with a symmetric subalgebra of $\mathfrak{g}$. So we can talk about…
We give a short and unified proof of the Brundan-Kleshchev isomorphism between blocks of cyclotomic Hecke algebras and cyclotomic KhovanovLauda-Rouquier algebras of type A.
We introduce a precise notion, in terms of few Schlessinger's type conditions, of extended deformation functors which is compatible with most of recent ideas in the Derived Deformation Theory (DDT) program and with geometric examples. With…
For C*-algebras $A$ and $B$, we generalize the notion of a quasihomomorphism from $A$ to $B$, due to Cuntz, by considering quasihomomorphisms from some C*-algebra $C$ to $B$ such that $C$ surjects onto $A$, and the two maps forming a…
We establish that Hitchin's connection exist for any rigid holomorphic family of Kahler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints. Using Toeplitz operators we prove…
We reformulate Heegaard Floer homology in terms of holomorphic curves in the cylindrical manifold Sigma x [0,1] x R, where Sigma is the Heegaard surface, instead of Sym^g(Sigma). We then show that the entire invariance proof can be carried…
We develop an obstruction theory for Hirsch extensions of cbba's with twisted coefficients. This leads to a variety of applications, including a structural theorem for minimal cbba's, a construction of relative minimal models with twisted…
We consider closed orientable hypersurfaces in a wide class of warped product manifolds, which include space forms, deSitter-Schwarzschild and Reissner-Nordstr\"{o}m manifolds. By using a new integral formula or Brendle's Heintze-Karcher…
Controlled topology is one of the main tools for proving the isomorphism conjecture concerning the algebraic $K$-theory of group rings. In this article we dive into this machinery in two examples: when the group is infinite cyclic and when…
Acyclic cluster algebras have an interpretation in terms of tilting objects in a Calabi-Yau category defined by some hereditary algebra. For a given quiver $Q$ it is thus desirable to decide if the cluster algebra defined by $Q$ is acyclic.…
Generalising a conjecture of Singerman, it is shown that there exist orientably regular chiral hypermaps of every non-spherical type. The proof uses the representation theory of automorphism groups acting on homology and on various spaces…
A wide class of q-deformed harmonic oscillators including those of Macfarlane type and of Dubna type is shown to be describable in a unified way. The Hamiltonian of the oscillator is assumed to be given by a q-deformed anti-commutator of…
This is the first in a series of papers in which we develop a twistor-based method of constructing hyperkaehler metrics from holomorphic functions and elliptic curves. As an application, we revisit the Atiyah-Hitchin manifold and derive in…
By the work of Li, a compact co-K\"ahler manifold $M$ is a mapping torus $K_\varphi$, where $K$ is a K\"ahler manifold and $\varphi$ is a Hermitian isometry. We show here that there is always a finite cyclic cover $\bar M$ of the form $\bar…
The distribution of the unipotent modules (in non-defining prime characteristic) of the finite unitary groups into Harish-Chandra series is investigated. We formulate a series of conjectures relating this distribution with the crystal graph…
The exact critical Casimir force between periodically deformed boundaries of a 2D semi-infinite strip is obtained for conformally invariant classical systems. Only two parameters (conformal charge and scaling dimension of a boundary…
We construct a new class of algebras resembling enveloping algebras and generalizing orthogonal Gelfand-Zeitlin algebras and rational Galois algebras studied by [EMV,FuZ,RZ,Har]. The algebras are defined via a geometric realization in terms…
We suggest a Hamiltonian formulation for the spin Ruijsenaars-Schneider system in the trigonometric case. Within this interpretation, the phase space is obtained by a quasi-Hamiltonian reduction performed on (the cotangent bundle to) a…