Arthur's Market

Arthur’s Market is a set of pages that allow you to explore -packets. It is based on Hiraku Atobe‘s implementation of -packets in SageMath. I converted a lot of the code from SageMath to HTML/TypeScript and made a friendly user interface, accessible to mathematicians working on -packets that are not necessarily familiar with SageMath or programming languages.

Please let me know if you find any bugs or if you have any ideas for features you would like to have!

• Arthur Packet Calculator - allows one to inspect the -packet of a given -parameter. 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 calculator - allows one 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 calculator - allows one 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.