Related papers: A classification of harmonic Maass forms
We classify simple Whittaker modules for classical Lie superalgebras in terms of their parabolic decompositions. We establish a type of Mili\v{c}i\'c-Soergel equivalence of a category of Whittaker modules and a category of Harish-Chandra…
We resolve a question of Kac, and explain the automorphic properties of characters due to Kac-Wakimoto pertaining to sl(m|n)^ highest weight modules, for n \geq 1. We prove that the Kac-Wakimoto characters are essentially holomorphic parts…
We give conditions for unitarizability of Harish-Chandra super modules for Lie supergroups and superalgebras.
Recently, K. Bringmann, P. Guerzhoy, Z. Kent and K. Ono studied the connection between Eichler integrals and the holomorphic parts of harmonic weak Maass forms on the full modular group. In this article, we extend their result to more…
We show that the support of a simple weight module over the Neveu-Schwarz algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all non-trivial weight spaces of such module are…
Recall that a Maass wave form on the full modular group Gamma=PSL(2,Z) is a smooth gamma-invariant function u from the upper half-plane H = {x+iy | y>0} to C which is small as y \to \infty and satisfies Delta u = lambda u for some lambda…
The aim of this paper is to describe efficient algorithms for computing Maass waveforms on subgroups of the modular group PSL(2,Z) with general multiplier systems and real weight. A selection of numerical results obtained with these…
In this paper, firstly we construct two classes of Lie conformal superalgebras denoted by $\mathcal{HVS}(\alpha)$ and $\mathcal{HVS}(\beta,\gamma,\tau)$, respectively, where $\alpha$ is an nonzero complex number and $\beta,\gamma,\tau$ are…
For a simple module $M$ over the positive part of the Virasoro algebra (actually for any simple module over some finite dimensional solvable Lie algebras $\mathfrak{a}_r$) and any $\alpha\in\C$, a class of weight modules $\mathcal {N}(M,…
The source of these notes is a series of lectures given at the CIMPA's summer school "Recent Topics in Geometric Analysis".
A well-known theorem of Mathieu's states that a Harish-chandra module over the Virasoro algebra is either a highest weight module, a lowest weight module or a module of the intermediate series. It is proved in this paper that an analogous…
It is shown that there are no simple mixed modules over the twisted N=1 Schr\"{o}dinger-Neveu-Schwarz algebra, which implies that every irreducible weight module over it with a nontrivial finite-dimensional weight space, is a Harish-Chandra…
We show that the support of an irreducible weight module over the $W$-algebra $W(2, 2)$, which has an infinite dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite…
Composite Higgs models provide an attractive solution to the hierarchy problem. However, many realistic models suffer from tuning problems in the Higgs potential. There are often large contributions from the UV dynamics of the composite…
Let p be a prime number. The Hasse invariant is a modular form modulo p that is often used to produce congruences between modular forms of different weights. We show how to produce such congruences between forms of weights 2 and p+1, in…
We construct two families of harmonic Maass Hecke eigenforms. This construction answers a question of Mazur about the existence of an "eigencurve-type" object in the world of harmonic Maass forms. Using these families, we construct $p$-adic…
Characteristic cycles,leading term cycles,associated varieties and Harish-Chandra cells are computed for the family of highest weight Harish-Chandra modules for Sp(2n, R) having regular integral infinitesimal character.
It is obtained that an irreducible weight module with finite weight multiplicities over a higher rank Virasoro or super-Virasoro algebra is either a module of the intermediate series, or a so-called finitely-dense module.
In this paper we introduce two new methods for constructing harmonic morphisms from solvable Lie groups. The first method yields global solutions from any simply connected nilpotent Lie group and from any Riemannian symmetric space of…
We twist Zagier's function $f_{k,D}$ by a sign function and a genus character. Assuming weight $0 < k \equiv 2 \pmod{4}$, and letting $D$ be a positive non-square discriminant, we prove that the obstruction to modularity caused by the sign…