Normalized Local Theta Correspondence and the Duality of Inner Product Formulas
نویسندگان
چکیده
We conjecture that local theta correspondence can be normalized by the leading coefficient of a weighted local period integral, and that there exists a duality of local and global inner product formulas. The conjecture is verified for the pair ( SL2, PGL2) and (SL2, SO(2, 2)). As an application, global inner product formulas are obtained for liftings in the directions PGL2 → SL2, GSO(2, 2) → GL2.
منابع مشابه
Atomic Systems in 2-inner Product Spaces
In this paper, we introduce the concept of family of local atoms in a 2-inner product space and then this concept is generalized to an atomic system. Besides, a characterization of an atomic system lead to obtain a new frame. Actually this frame is a generalization of previous works.
متن کاملq-Hypergeometric Series and Macdonald Functions
Abstract We derive a duality formula for two-row Macdonald functions by studying their relation with basic hypergeometric functions. We introduce two parameter vertex operators to construct a family of symmetric functions generalizing Hall-Littlewood functions. Their relation with Macdonald functions is governed by a very well-poised q-hypergeometric functions of type 4 0$, for which we obtain ...
متن کامل0 O ct 1 99 4 EXPLICIT FORMULAS FOR THE WALDSPURGER AND BESSEL MODELS
In this paper we will study certain models of irreducible admissible representations of the split special orthogonal group SO(2n + 1) over a nonarchimedean local field. If n = 1, these models were considered by Waldspurger [Wa1,Wa2], and arose in his profound studies of the Shimura correspondence. If n = 2, they were considered by Novodvorsky and Piatetski-Shapiro [NP], who called them Bessel m...
متن کاملA Comparative Study of Fuzzy Inner Product Spaces
In the present paper, we investigate a connection between two fuzzy inner product one of which arises from Felbin's fuzzy norm and the other is based on Bag and Samanta's fuzzy norm. Also we show that, considering a fuzzy inner product space, how one can construct another kind of fuzzy inner product on this space.
متن کاملTempered Representations and the Theta Correspondence
Let V be an even dimensional nondegenerate symmetric bilinear space over a nonarchimedean local field F of characteristic zero, and let n be a nonnegative integer. Suppose that σ ∈ Irr(O(V )) and π ∈ Irr(Sp(n, F )) correspond under the theta correspondence. Assuming that σ is tempered, we investigate the problem of determining the Langlands quotient data for π. Let F be a nonarchimedean local f...
متن کامل