Non-archimedean local A-packets
This set of apps allows you to explore non-archimedean local -packets. It was formerly known as Arthur's Market. The implementation is a TypeScript port of Hiraku Atobe's implementation of -packets in SageMath and of the extension by Alexander Hazeltine, Baiying Liu and Chi-Heng Lo. Most of the port was created by Elad Zelingher in March 2024 with the assistance of ChatGPT.
Below are some inputs (and references for these inputs) that are worth trying!
- Arthur Packets - allows you to inspect the -packet of a given -parameter of good parity. Try the input (1,6), (1,2), (4,1) or the input (4,6), (3,3)! These correspond to Examples 3.8 and 3.9 in the paper Construction of local A-packets by Hiraku Atobe.
- Extended multisegment inspector - allows you to inspect a given extended multisegment. You can see the representation this extended multisegment defines, the -packets it belongs to, its dual and more! Try the input (([3,1], 0, -), ([5,2], 1, -), ([6,3], 2, -), ([5,4], 0, -)) that corresponds to Example 3.2 in loc. cit.
- Representation inspector - allows you to determine if a given representation is of Arthur type. In case it is of Arthur type, this page allows one to see the different extended multisegments that define the representation. Try the input [-1/2, -5/2], [-1/2, -1/2], [3/2, -5/2] and (2,4,6), (1,-1,-1) that corresponds to Section 3.5 case 4 in the paper The set of local A-packets containing a given representation by Hiraku Atobe.
📄️ Arthur Packets
Lists elements in a local A packet
📄️ Adams conjecture
Lists theta lifts of elements in a local A packet
📄️ Extended multisegment inspector
Displays details regarding extended multisegments
📄️ Representation inspector
Finds all local A-packets containing a given representation