Related papers: Regular functions on the Shilov boundary
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
Let G=SU(2) and let \Omega G denote the space of continuous based loops in G, equipped with the pointwise conjugation action of G. It is a classical fact in topology that the ordinary cohomology H^*(\Omega G) is a divided polynomial algebra…
We consider the notion of a confluent spherical function on a connected semisimple Lie group, $G,$ with finite center and of real rank $1,$ and discuss the properties and relationship of its algebra with the well-known Schwartz algebra of…
We consider the Dirichlet problem for solutions to general second-order homogeneous elliptic equations with constant complex coefficients. We prove that any Jordan domain with $C^{1,\alpha}$-smooth boundary, $0<\alpha<1$, is not regular…
Pairing between the universal enveloping algebra $U_q(sl(2))$ and the algebra of functions over $SL_q(2)$ is obtained in explicit terms. The regular representation of the quantum double is constructed and investigated. The structure of the…
This paper develops the geometry of locally bounded rational functions on non-singular real algebraic varieties. First various basic geometric and algebraic results regarding these functions are established in any dimension, culminating…
We provide a systematic treatment of boundaries based on subgroups $K\subseteq G$ with the Kitaev quantum double $D(G)$ model in the bulk. The boundary sites are representations of a $*$-subalgebra $\Xi\subseteq D(G)$ and we explicate its…
We introduce a new Banach algebra ${\mathcal A}({\mathbb C}_+)$ of bounded analytic functions on ${\mathbb C}_+=\{z\in{\mathbb C}\, :\, {\rm Re}(z)>0\}$ which is an analytic version of the Figa-Talamenca-Herz algebras on ${\mathbb R}$. Then…
The ring of symmetric functions can be implemented in the homology of \union_{a,b} Gr(a,a+b), the multiplicative structure being defined from the "direct sum" map. There is a natural circle action (simultaneously on all Grassmannians) under…
We discuss linear algebra of infinite-dimensional vector spaces in terms of algebraic (Hamel) bases. As an application we prove the surjectivity of a large class of linear partial differential operators with smooth ($\mathcal…
For $\g=sl(n)$ we construct a two parametric $U_h(\g)$-invariant family of algebras, $(S\g)_{t,h}$, which defines a quantization of the function algebra $S\g$ on the coadjoint representation and in the parameter $t$ gives a quantization of…
We describe the graded characters and Hilbert functions of certain graded artinian Gorenstein quotients of the polynomial ring which are also representations of the symmetric group. Specifically, we look at those algebras whose socles are…
We show that the algebra $D_\hbar(SL_n/U)$ of differential operators on the base affine space of $SL_n$ is the quantized Coulomb branch of a certain 3d $\mathcal{N} = 4$ quiver gauge theory. In the semiclassical limit this proves a…
A garland based on a manifold $P$ is a finite set of manifolds homeomorphic to $P$ with some of them glued together at marked points. Fix a manifold $M$ and consider a space $\NN$ of all smooth mappings of garlands based on $P$ into $M$. We…
We establish the theorems that give necessary and sufficient conditions for an arbitrary function defined in the unit disk of complex plane in order to has boundary values along classes of equivalencies of simple curves. Our results…
It is studied the Classification Problem for Formal (Holomorphic) Embeddings between (open pieces of) Shilov Boundaries of Bounded Symmetric Domains of First Type.
The representation theory of symmetric Lie superalgebras and corresponding spherical functions are studied in relation with the theory of the deformed quantum Calogero-Moser systems. In the special case of symmetric pair g=gl(n,2m),…
The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie…
For central simple finitely generated algebras of finite Gelfand-Kirillov dimension and for their division algebras upper bounds are obtained for the transcendence degree of their commutative subalgebras and subfields respectively. In the…
The Hilbert functions and the regularity of the graded components of local cohomology of a bigraded algebra are considered. Explicit bounds for these invariants are obtained for bigraded hypersurface rings.