MULTIPLICITY ONE FOR THE PAIR (GLn(D);GLn(E))

Kostka multiplicity one for multipartitions

If [λ(j)] is a multipartition of the positive integer n (a sequence of partitions with total size n), and μ is a partition of n, we study the number K[λ(j)]μ of sequences of semistandard Young tableaux of shape [λ(j)] and total weight μ. We show that the numbers K[λ(j)]μ occur naturally as the multiplicities in certain permutation representations of wreath products. The main result is a set of ...

Strong Multiplicity One for the Selberg Class

In [7] A. Selberg axiomatized properties expected of L-functions and introduced the “Selberg class” which is expected to coincide with the class of all arithmetically interesting L-functions. We recall that an element F of the Selberg class S satisfies the following axioms. • In the half-plane σ > 1 the function F (s) is given by a Dirichlet series ∑∞n=1 aF (n)n with aF (1) = 1 and aF (n) ≪ǫ n ...

Effective Strong Multiplicity One for Gl M

On Strong Multiplicity One for Automorphic Representations

We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let π be a unitary, cuspidal, automorphic representation of GLn(AK). Let S be a set of finite places of K, such that the sum ∑ v∈S Nv −2/(n+1) is convergent. Then π is uniquely determined by the collection of the local components {πv | v 6∈ S, v finite} of π. Combining this theorem with base change, it is p...

Multiplicity Preservation for Orthogonal-symplectic and Unitary Dual Pair Correspondences

Over a non-archimedean local field of characteristic zero, we prove the multiplicity preservation for orthogonal-symplectic dual pair correspondences and unitary dual pair correspondences.