Related papers: The Maass Space for Paramodular Groups

We notice that for any positive integer $k$, the set of $(1,2)$-specialized characters of level $k$ standard $A_{1}^{(1)}$-modules is the same as the set of rescaled graded dimensions of the subspaces of level $2k+1$ standard…

For a semisimple real Lie group $G$, we study topological properties of moduli spaces of polystable parabolic $G$-Higgs bundles over a Riemann surface with a divisor of finitely many distinct points. For a split real form of a complex…

We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.

Let $W$ be a Coxeter group and let $M$ be the free $Z[v,v^{-1}]$-module with basis indexed by the involutions of $W$. We show how recent results of Elias and Williamson on Soergel bimodules can be used to give an alternative definition of…

Let S_{w+2}(\Gamma_0(N)) be the vector space of cusp forms of weight w+2 on the congruence subgroup \Gamma_0(N). We first determine explicit formulas for period polynomials of elements in S_{w+2}(\Gamma_0(N)) by means of Bernoulli…

We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ${\mathbb Q}$, acting on…

This paper characterises the subspaces of $H^2(\mathbb D)$ simultaneously invariant under $S^2 $ and $S^{2k+1}$, where $S$ is the unilateral shift, then further identifies the subspaces that are nearly invariant under both $(S^2)^*$ and…

Let $G:=SO(2n)$ be the even special orthogonal group over $\mathbb{C}$ and let $M_{2n}^+$ (resp. $M_{2n}^-$) be the space of symmetric (resp. skew-symmetric) complex matrices with respect to the usual transposition. We study the structure…

Let $R$ be a semilocal principal ideal domain. Two algebraic objects over $R$ in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all…

Let G be a discrete group and $\Gamma$ an almost normal subgroup. The operation of cosets concatanation extended by linearity gives rise to an operator system that is embeddable in a natural C* algebra. The Hecke algebra naturally embeds as…

We research the location of the zeros of the Eisenstein series and the modular functions from the Hecke type Faber polynomials associated with the normalizers of congruence subgroups which are of genus zero and of level at most twelve. In…

In this paper, we study the quantum channel on a von Neuamnn algebra $\mathcal{M}$ preserving a von Neumann subalgebra $\mathcal{N}$, namely an $\mathcal{N}$-$\mathcal{N}$-bimodule unital completely positive map. By introducing the relative…

In this article we prove conditions under which a certain parabolic group cohomology space over a finite field F is a faithful module for the Hecke algebra of Katz modular forms over an algebraic closure of F. These results can e.g. be used…

We construct explicit geometric models for moduli spaces of semi-stable strongly parabolic Higgs bundles over the Riemann sphere, in the case of rank two, four marked points, arbitrary degree, and arbitrary weights. The mechanism of…

The classification of the Einstein spaces with the Stackel metric of the (3.0) has been done. These spaces are invariant under the action of the three-parameter abelian group of motions and belong to the first type Bianchi spaces. Thus the…

Quantum mechanical systems with position dependent masses (PDM) admitting for and more dimensional symmetry algebras are classified. Namely, all PDM systems are specified which, in addition to their invariance w.r.t. a three parametric Lie…

We propose an algebraic definition of the space of l-new mod-p modular forms for Gamma0(Nl) in the case that l is prime to N, which naturally generalizes to a notion of newforms modulo p in squarefree level. We use this notion of newforms…

In this paper we generalise the notion of Drinfeld modular form for the group $\Gamma$ := GL2(Fq[$\theta$]) to a vector-valued setting, where the target spaces are certain modules over positive characteristic Banach algebras over which are…

Using a noncommutative analog of Chevalley's decomposition of polynomials into symmetric polynomials times coinvariants due to Bergeron, Reutenauer, Rosas, and Zabrocki we compute the graded Frobenius series for their two sets of…

We give a complete proof of the Maass-Selberg relations for Whittaker integrals on a real reductive group. These relations were asserted In unpublished work of Harish-Chandra, and proven in the basic setting of maximal parabolic parabolic…