Related papers: Resolvent algebra in Fock-Bargmann representation

In this paper, we study the algebraic symplectic geometry of the singular moduli spaces of Higgs bundles of degree $0$ and rank $n$ on a compact Riemann surface $X$ of genus $g$. In particular, we prove that such moduli spaces are…

We introduce the symplectic group $\mathrm{Sp}_2(G, \sigma)$ associated to a Lie subgroup $G$ of a (possibly noncommutative) associative algebra $A$ equipped with an anti-involution $\sigma$. Our construction recovers several classical Lie…

We introduce a new class of algebras called Poisson orders. This class includes the symplectic reflection algebras of Etingof and Ginzburg, many quantum groups at roots of unity, and enveloping algebras of restricted Lie algebras in…

We construct a representation of each finitely aligned aperiodic k-graph \Lambda\ on the Hilbert space H^{ap} with basis indexed by aperiodic boundary paths in \Lambda. We show that the canonical expectation on B(H^{ap}) restricts to an…

Let G be a finite group acting on a symplectic complex vector space V. Assume that the quotient V/G has a holomorphic symplectic resolution. We prove that G is generated by "symplectic reflectionsd"', i.e. symplectomorphisms with fixed…

Finiteness spaces constitute a categorical model of Linear Logic (LL) whose objects can be seen as linearly topologised spaces, (a class of topological vector spaces introduced by Lefschetz in 1942) and morphisms as continuous linear maps.…

We start from a noncompact Lie algebra isomorphic to the Dirac algebra and relate this Lie algebra in a brief review to low energy hadron physics described by the compact group SU(4). This step permits an overall physical identification of…

Beilinson--Bernstein localisation relates representations of a Lie algebra $\mathfrak{g}$ to certain $\mathcal{D}$-modules on the flag variety of $\mathfrak{g}$. In [arXiv:2002.01540], examples of $\mathfrak{sl}_2$-representations which…

Suppose $(M,\omega)$ is a compact symplectic manifold acted on by a compact Lie group $K$ in a Hamiltonian fashion, with moment map $\mu: M \to \Lie(K)^*$ and Marsden-Weinstein reduction $M_{red} = \mu^{-1}(0)/K$. In this paper, we assume…

A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine…

A relatively compressed algebra with given socle degrees is an Artinian quotient $A$ of a given graded algebra $R/\fc$, whose Hilbert function is maximal among such quotients with the given socle degrees. For us $\fc$ is usually a…

We develop notions of a representation of a topological graph E and of a covariant representation of a topological graph E which do not require the machinery of C*-correspondences and Cuntz-Pimsner algebras. We show that the C*-algebra…

One of the major questions in the theory of Toeplitz operators on the Bergman space over the unit disk $\mathbb D$ in the complex plane $\mathbb C$ is a complete description of the commutant of a given Toeplitz operator, that is the set of…

In this paper we study overcomplete systems of coherent states associated to compact integral symplectic manifolds by geometric quantization. Our main goals are to give a systematic treatment of the construction of such systems and to…

In this article, we first briefly introduce the history of the Weil-\'etale cohomology theory of arithmetic schemes and review some important results established by Lichtenbaum, Flach and Morin. Next we generalize the Weil-etale cohomology…

In the context of Loop Quantum Gravity (LQG), we study the fate of Thiemann complexifier in homogeneous and isotropic FRW cosmology. The complexifier is the dilatation operator acting on the canonical phase space for gravity and generates…

We survey some of the known results on the relation between the homology of the {\em full} Hecke algebra of a reductive $p$-adic group $G$, and the representation theory of $G$. Let us denote by $\CIc(G)$ the full Hecke algebra of $G$ and…

We consider the stochastic reflection problem associated with a self-adjoint operator $A$ and a cylindrical Wiener process on a convex set $K$ with nonempty interior and regular boundary $\Sigma$ in a Hilbert space $H$. We prove the…

In this article, we produce Grothendieck-Riemann-Roch formulas for cohomology theories that are not oriented in the classical sense. We then specialize to the case of cohomology theories that admit a so-called symplectic orientation and…

Let $\Sigma_{g,n}$ be a compact oriented surface of genus $g$ with $n$ open disks removed. The algebra $\mathcal{L}_{g,n}(H)$ was introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche and is a combinatorial quantization of the moduli…