Two of the primary methods of constructing automorphic forms are the Langlands program and Howe's theory of dual pairs. The Langlands program concerns a reductive linear group G deened over a number eld. Associated to G is its dual group L G. The con-jectural principle of functoriality says that a homomorphism L H ! L G should provide a \transfer" of automorphic representations from H to those ...

We describe the construction of vector valued modular forms transforming under a given congruence representation of the modular group SL(2,Z) in terms of theta series. We apply this general setup to obtain closed and easily computable formulas for conformal characters of rational models of W-algebras. 2 Université Bordeaux I, UFR de Mathématiques et Informatiques, 351 rue de la Libération, 3340...

for any lacunary sequence $theta = (k_{r})$, we define the concepts of $s_{theta}-$limit point and $s_{theta}-$cluster point of a sequence of fuzzy numbers $x = (x_{k})$. we introduce the new sets  $lambda^{f}_{s_{theta}}(x)$, $gamma^{f}_{s_{theta}}(x)$ and prove some inclusion relaions between these and the sets $lambda^{f}_{s}(x)$, $gamma^{f}_{s}(x)$ introduced in ~cite{ayt:slpsfn} by aytar [...

Let K be a quadratic imaginary field and π an irreducible regular algebraic cuspidal automorphic representation of GL(2,AK). Under the assumption that the central character χπ is isomorphic to its complex conjugate, Taylor et al. associated p-adic Galois representations ρπ,p : GK → GL(2,Qp) which are unramified except at finitely many places, and such that the truncated L-function of the Galois...

Str. Case [+SC +HR –LR ] [+SC –HR –LR ] [–SC –HR +LR ] Morph. Str. Case [ ] [–HR,–LR] — Abstract case features function as constraints on morphosyntactic case. A theta-role’s abstract case must optimally match the argument’s morphosyntactic case. Because they are categorized by the same features, the relation between these two levels of representation can be established by general principlescas...

Theta correspondence y over R is established by Howe (J. Amer. Math. Soc. 2 (1989) 535). In He (J. Funct. Anal. 199 (2003) 92), we prove that y preserves unitarity under certain restrictions, generalizing the result of Li (Invent. Math. 97 (1989) 237). The goal of this paper is to elucidate the idea of constructing unitary representation through the propagation of theta correspondences. We show...

Temporal coding is a means of representing information by the time, as opposed to the rate, at which neurons fire. Evidence of temporal coding in the hippocampus comes from place cells, whose spike times relative to theta oscillations reflect a rat’s position while running along stereotyped trajectories. This arises from the backwards shift in cell firing relative to local theta oscillations (p...

The primary aim of this review is to examine evidence for a functional role of gamma and theta oscillations in human episodic memory. It is proposed here that gamma and theta oscillations allow for the transient interaction between cortical structures and the hippocampus for the encoding and retrieval of episodic memories as described by the hippocampal memory indexing theory (Teyler and DiScen...

The representation of mouse alloantigens belonging to three systems, H-2, theta and TL, on the surface of cells from thymus, spleen, lymph nodes, and peritoneal cavity, was studied by electron microscopy with ferritin-labeled antibody. As expected from earlier serological data, TL was confined to thymocytes, theta was found on thymocytes and lymphocytes, and H-2 occurred to some extent on all c...

The quantum mechanical propagators of the linear automorphisms of the two-torus (cat maps) determine a projective unitary representation of the theta group Γ θ ⊂ SL(2, Z). We prove that there exists an appropriate choice of phases in the propagators that defines a proper representation of Γ θ. We also give explicit formulae for the propagators in this representation.