Related papers: Tannaka-Krein duality for compact groupoids II, Fo…

We provide a fundamental domain for the action of the finite Weyl group on a maximal torus of a compact Lie group of the corresponding type. The general situation is reduced to the adjoint case and, from the perspective of root data, this…

We introduce the category of set-theoretic representations of a matched pair of groupoids. This is a monoidal category endowed with a monoidal functor to the category of quivers over the common base of the groupoids in the matched pair (the…

This is an introduction to the geometry of compact Riemann surfaces, largely following the books Farkas-Kra, Fay, Mumford Tata lectures. 1) Defining Riemann surfaces with atlases of charts, and as locus of solutions of algebraic equations.…

For a simple Lie algebra g we consider an analogue of the affine algebra ^gk with n singularities, defined starting from the ring of functions on the n-pointed disk. We study the center of its completed enveloping algebra and prove an…

We give a further extension and generalization of Dedekind's theorem over those presented by Yamaguchi. In addition, we give two corollaries on irreducible representations of finite groups and a conjugation of the group algebra of the…

The Riesz transform of $u$ : $\mathcal{S}(\mathbb{R}^n) \rightarrow \mathcal{S'}(\mathbb{R}^n)$ is defined as a convolution by a singular kernel, and can be conveniently expressed using the Fourier Transform and a simple multiplier. We…

In this paper, we prove an exponential integral formula for the Fourier transform of Bessel functions over complex numbers, along with a radial exponential integral formula. The former will enable us to develop the complex spectral theory…

In this article, we study the various fundamental groupoid schemes corresponding to Tannakian categories of certain types of vector bundles. We compute fundamental groupoid scheme of anisotropic conic, Klein bottle and abelian varieties.…

Like quantum groups, quantum groupoids frequently appear in pairs of mutually dual objects. We develop a general Pontrjagin duality theory for quantum groupoids in the algebraic setting that extends Van Daele's duality theory for multiplier…

This paper presents non-commutative and structural notions of torsor. The two are related by the machinery of Tannaka-Krein duality.

Jeffery's 1861 computations using finite difference calculus are resurrected and extended from forward differences to general delta operators and used to neatly prove theorems in the Rota--Mullins theory of polynomials of binomial type…

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r)…

In this work, we introduce a class of Timmermann's measured multiplier Hopf *-algebroids called algebraic quantum transformation groupoids of compact type. Each object in this class admits a Pontrjagin-like dual called an algebraic quantum…

We discuss an interesting duality known to occur for certain complex reflection groups, namely the duality groups. Our main construction yields a concrete, representation theoretic realisation of this duality. This allows us to naturally…

We study irreducible spherical unitary representations of the Drinfeld double of a $q$-deformation of a connected simply connected compact Lie group, which can be considered as a quantum analogue of the complexification of the Lie group. In…

Assuming the standard framework of mirror symmetry, a conjecture is formulated describing how the diffeomorphism group of a Calabi-Yau manifold Y should act by families of Fourier-Mukai transforms over the complex moduli space of the mirror…

Double groupoids are a type of higher groupoid structure that can arise when one has two distinct groupoid products on the same set of arrows. A particularly important example of such structures is the irrational torus and, more generally,…

Consider the Fourier transform on the group $GL(2,R)$ of real $2\times 2$-matrices. We show that Fourier-images of polynomial differential operators on $GL(2,R)$ are differential-difference operators with coefficients meromorphic in…

We give a new alternative version of the reconstruction procedure for ergodic actions of compact quantum groups and we refine it to include characterizations of (braided commutative) Yetter-Drinfeld C*-algebras. We then use this to…

We consider the representation space of a compact surface, that is the space of morphisms from the fundamental group to SU(2) up to conjugation. We show that the trace functions associated to multicurves on the surface are linearly…