相关论文: The Weil representation and Hecke operators for ve…
We review some facts about the representation theory of the Hecke algebra. We adapt for the Hecke algebra case the approach of Okounkov and Vershik which was developed for the representation theory of symmetric groups. We justify an…
We carry out some computations of vector valued Siegel modular forms of degree two, weight (k,2) and level one. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an…
In a previous work the authors gave a conceptual explanation for the linearity of the Weil representation over a finite field k of odd characteristic: There exists a canonical system of intertwining operators between the Lagrangian models…
We introduce a method for producing vector-valued automorphic forms on unitary groups from scalar-valued ones. As an application, we construct an explicit example. Our strategy employs certain differential operators. It is inspired by work…
We present explicit formulas for Hecke eigenforms as linear combinations of q-analogues of modified double zeta values. As an application, we obtain period polynomial relations and sum formulas for these modified double zeta values. These…
The $GL_{\ell+1}(\mathbb{R})$ Hecke-Baxter operator was introduced as an element of the $O_{\ell+1}$-spherical Hecke algebra associated with the Gelfand pair $O_{\ell+1}\subset GL_{\ell+1}(\mathbb{R})$. It was specified by the property to…
In this article we show that 'most' of the vector valued modular forms w.r.t. the Weil representation on the groups rings $\mathbb{C}[D]$ of discriminant forms D are oldforms. The precise meaning of oldform is that the form can be…
Hecke operators acting on modular functions arise naturally in the context of 2d conformal field theory, but in seemingly disparate areas, including permutation orbifold theories, ensembles of code CFTs, and more recently in the context of…
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…
We study the action of the formal affine Hecke algebra on the formal group algebra, and show that the the formal affine Hecke algebra has a basis indexed by the Weyl group as a module over the formal group algebra. We also define a concept…
The modular representation theory of finite groups has its origins in the work of Richard Brauer. In this survey article we first discuss the work being done on some outstanding conjectures in the theory. We then describe work done in the…
Using techniques from the theory of mock modular forms and harmonic Maass forms, especially Weierstrass mock modular forms, we establish several dimension formulas for certain strongly rational, holomorphic vertex operator algebras,…
This is a survey paper about affine Hecke algebras. We start from scratch and discuss some algebraic aspects of their representation theory, referring to the literature for proofs. We aim in particular at the classification of irreducible…
In this paper, we discuss the theory of the Siegel modular variety in the aspects of arithmetic and geometry. This article covers the theory of Siegel modular forms, the Hecke theory, a lifting of elliptic cusp forms, geometric properties…
We describe a new link between the theory of topological modular forms and representations of vertex operator algebras obtained by certain lattices. The construction is motivated by the arithmetic Whitehead tower of the orthogonal groups.…
We construct a class of representations of the Heisenberg algebra in terms of the complex shift operators subject to the proper continuous limit imposed by the correspondence principle. We find a suitable Hilbert space formulation of our…
We study the character of the infinite wedge projective representation of the algebra of differential operators on the circle. We prove quasi-modularity of this character and also compute certain generating functions for traces of…
We prove a mean value theorem for the traces of Hecke operators acting on cusp forms of GL(n) over imaginary quadratic number fields together with an upper bound for the error term depending explicitly on the Hecke operator.
The purpose of this paper is to give an overview of the operator structure of frames, where the operator belongs to certain classes of linear operators and the element belongs to $H$. We discuss the size of the set of such elements. Also,…
New identities on traces of representations of the Hecke algebra on the spaces of paths on graphs are presented. These identities are relevant in the computation of partition functions with fixed boundary conditions and of two-point…