Characters, genericity, and multiplicity one for U(3)

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 ...

Multiplicity-Free Permutation Characters in GAP

This note shows a few examples of GAP computations concerning multiplicity-free permutation characters, with an emphasis on the classification of the faithful multiplicity-free permutation characters of the sporadic simple groups and their automorphism groups given in [BL96]. For examples on GAP computations with permutation characters in general, see the note [Bre]. For further questions about...

Equality Of Multiplicity Free Skew Characters

In this paper we show that two skew diagrams λ/μ and α/β can represent the same multiplicity free skew character [λ/μ] = [α/β] only in the the trivial cases when λ/μ and α/β are the same up to translation or rotation or if λ = α is a staircase partition λ = (l, l − 1, . . . , 2, 1) and λ/μ and α/β are conjugate of each other.

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...