C*-Algebraic Intertwiners for Degenerate Principal Series of Special Linear Groups

The author constructs unitary intertwiners for degenerate C＊-algebraic uni- versal principal series of SL（n＋ 1） over a local field by explicitely normalizing standard intertwining integrals at the level of Hilbert modules.     

Multi-variable Hermite matrix polynomials: Properties and applications

In this paper, the multi-variable Hermite matrix polynomials are introduced by algebraic decomposition of exponential operators. Their properties are established using operational methods. The matrix forms of the Chebyshev and truncated polynomials of two variable are also introduced, which are further used to derive certain operational representations and expansion formulae.     

Commutativity of the Valdivia–Vogt table of representations of function spaces

In this article, we show that the Valdivia–Vogt structure table—containing the sequence space representations of the most used spaces of smooth functions appearing in the theory of distributions—can be interpreted as a commutative diagram, i.e., there is an isomorphism between the space of infinitely differentiable functions and the space , where s is the space of rapidly decreasing sequences, such that its restriction to the other function spaces in the structure table yields an isomorphism between these spaces of smooth functions and their sequence space representation. This result answers the corresponding question of Prof. Dietmar Vogt formulated on the conference “Functional Analysis: Applications to Complex Analysis and Partial Differential Equations” held in B?dlewo in May 2012.     

Anisotropic shearlet transforms for L2

In this paper, we present a new anisotropic generalization of the continuous shearlet transformation. This is achieved by means of an explicit construction of a family of reproducing Lie subgroups of the symplectic group. We study the properties of this new family of anisotropic shearlet transformations. In particular, we provide an analog of the Calderón admissibility condition for anisotropic shearlet reproducing functions.     

Towards a classification of global integral constructions and functorial liftings using the small representations method

This is a survey article in which we discuss some recent approach toward the classification of global factorizable integrals, and constructions of Langlands functorial lifting using small representations. To do that we use the language of unipotent orbits and their relation to Fourier coefficients. We also introduce the dimension equation, and set our goal to classify all global integrals of a certain form which satisfies this equation.     

Square integrability of representations on p-adic symmetric spaces

A symmetric space analogue of Casselman's criterion for square integrability of representations of a p-adic group is established. It is described in terms of exponents of Jacquet modules along parabolic subgroups associated to the symmetric space.     

Central Pairs, Galois Theory and Automorphic Forms

A central pair over a field k of characteristic 0 consists of a finite Abelian group which is equipped with a central 2-cocycle with values in the multiplicative group k ^* of k. In this paper we use specific central pairs to construct a class of projective representations of the absolute Galois group G _k of k and if k is a number field we investigate the liftings of these projective representations to linear representations of G _k . In particular we relate these linear representations to automorphic representations. It turns out that some of these automorphic representations correspond to certain indefinite modular forms already constructed by E. Hecke.     

Hilbert-Space Representations of a Cross-Product Algebra Related to the 3D-Calculus on O(SU q (1,1))

Hilbert-space representations of the right cross-product *-algebra of the quantum SU(1,1) with a *-algebra related to Woronowicz's 3D-calculus on the quantum SU(1,1) are studied and classified.     

Music as Embodied Mathematics: A Study of a Mutually Informing Affinity

The argument examined in this paper is that music – when approached through making and responding to coherent musical structures,facilitated by multiple, intuitively accessible representations – can become a learning context in which basic mathematical ideas can be elicited and perceived as relevant and important. Students' inquiry into the bases for their perceptions of musical coherence provides a path into the mathematics of ratio,proportion, fractions, and common multiples. Ina similar manner, we conjecture that other topics in mathematics – patterns of change,transformations and invariants – might also expose, illuminate and account for more general organizing structures in music. Drawing on experience with 11–12 year old students working in a software music/math environment, we illustrate the role of multiple representations, multi-media, and the use of multiple sensory modalities in eliciting and developing students' initially implicit knowledge of music and its inherent mathematics. This revised version was published online in July 2006 with corrections to the Cover Date.