Papers › On the intersection of local Arthur packets for classical groups and applications
On the intersection of local Arthur packets for classical groups and applications
Alexander Hazeltine, Baiying Liu, Chi-Heng Lo
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In this paper, for symplectic and split odd special orthogonal groups, we develop an account of theory on the intersection problem of local Arthur packets. Specifically, following Atobe's reformulation on M{\oe}glin's construction of local Arthur packets, we give a complete set of operators on the construction data, based on which, we provide algorithms and Sage codes to determine whether a given representation is of Arthur type. Furthermore, for any representation π of Arthur type, we give a precise formula for the set Ψ(π)={ local Arthur parameter ψ | the local Arthur packet Π_ψ contains π}. Our results have many applications, including the precise counting of tempered representations in any local Arthur packet, specifying and characterizing "the" local Arthur parameter in Ψ(π) for π, especially when π belongs to several local Arthur packets but does not belong to any local L-packet of Arthur type.
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