Related papers: On representations of real Jacobi groups

Let $A$ be a commutative unital $\mathbb{R}$-algebra and let $\rho$ be a seminorm on $A$ which satisfies $\rho(ab)\leq\rho(a)\rho(b)$. We apply T. Jacobi's representation theorem to determine the closure of a $\sum A^{2d}$-module $S$ of $A$…

In this paper, we outline a developement of the theory of orbit method for representations of real Lie groups. In particular, we study the orbit method for representations of the Heisenberg group and the Jacobi group.

For a smooth projective unitary representation of a locally convex Lie group G, the projective space of smooth vectors is a locally convex Kaehler manifold. We show that the action of G on this space is weakly Hamiltonian, and lifts to a…

We show that for every representation $ \rho : \pi_{1} (S_{g}) \to \text{Isom}(X) $ of the fundamental group of a genus $ g \ge 2 $ surface to the isometry group of a complete $ \text{CAT}(-1) $ metric space $ X $ there exists a Fuchsian…

We consider functors from the category of locally convex algebras to abelian groups and prove invariance under smooth homotopies for weakly J-stable algebras, where J is a harmonic operator ideal. This applies in particular to negative…

We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the…

Smooth modules for affine Kac-Moody algebras have a prime importance for the quantum field theory as they correspond to the representations of the universal affine vertex algebras. But, very little is known about such modules beyond the…

In $G$-equivariant stable homotopy theory, it is known that the equivariant Eilenberg-Mac Lane spectra representing ordinary equivariant cohomology have nontrivial $RO(G)$-graded homotopy corresponding to the equivariant (co)homology of…

This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations…

We define a generalized Jacobian $\mathrm{J}_\mathfrak{m}(\mathit{Gr})$ and a generalized Picard group $\mathrm{P}_\mathfrak{m}(\mathit{Gr})$ of a graph $\mathit{Gr}$ with respect to a modulus $ \mathfrak{m}=\sum_{i=1}^s m_iw_i$ with $w_i$…

We develop the rudiments of a finite-dimensional representation theory of groups over idempotent semifields by considering linear actions on tropical linear spaces. This can be considered a tropical representation theory, a characteristic…

There are many families of functions on partitions, such as the shifted symmetric functions, for which the corresponding q-brackets are quasimodular forms. We extend these families so that the corresponding q-brackets are quasimodular for a…

Let W be a smooth complex quasiprojective variety with the action of a connected reductive group G. Adapting the stratification approach of Teleman to a microlocal context, we prove a vanishing theorem for the functor of G-invariant…

We consider the action of a real linear algebraic group $G$ on a smooth, real affine algebraic variety $M\subset \R^n$, and study the corresponding left regular $G$-representation on the Banach space $C_0(M)$ of continuous, complex valued…

Let $G$ be a compact connected semisimple Lie group, let $K$ be a closed subgroup of $G$, let $\Gamma$ be a finite subgroup of $G$, and let $\tau$ be a finite-dimensional representation of $K$. For $\pi$ in the unitary dual $\widehat G$ of…

For a connected quasi-split reductive algebraic group $G$ over a field $k$, which is either a finite field or a non-archimedean local field, $\theta$ an involutive automorphism of $G$ over $k$, let $K =G^\theta$. Let $K^1=[K^0,K^0]$, the…

We set up operadic foundations for equivariant iterated loop space theory. We start by building up from a discussion of the approximation theorem and recognition principle for V-fold loop G-spaces to several avatars of a recognition…

We attempt to generalize the $p$-modular representation theory of finite groups to finite transporter categories, which are regarded as generalized groups. We shall carry on our tasks through modules of transporter category algebras, a type…

Let U be a smooth quasi-projective variety over a field k that is finite, the algebraic closure of a finite field or algebraically closed of characteristic 0. Let X be a suitable projective compactification of U, and D an effective divisor…

We develop a general framework for studying Abelian categories arising in isomeric representation theory, that is, representation theory broadly related to the supergroup Q(n). In this first part, we introduce notions of isomeric Heisenberg…