Non-archimedean local A-packets

This set of apps allows you to explore non-archimedean local $A$ -packets. It was formerly known as Arthur's Market. The implementation is a TypeScript port of Hiraku Atobe's implementation of $A$ -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!

Depth-Zero L-Packets lists normalized enhancements, ordered finite compact types, and induction data for tame parameters of Sp, odd SO, and unramified U, with symbolic $q$ . Try the singular four-member Sp₈ packet or the 16-member quadratic Sp₁₀ packet.
Depth-Zero Representation Inspector reconstructs the parameter and displays the packet from ordered finite compact types, admissible triples, and general-linear factors. Examples include Lust–Stevens's nonhyperspecial types and Kaletha's regular construction.
ABV Packets for GLₙ computes packets from multisegments using Cunningham's geometric description, with exact microlocal calculations in the browser. Try the Arthur singleton input (2,0),(1,-1/2),(1,1/2), the GL₆ input (3,0),(1,0),(2,3/2) for an exact calculation, the GL₈ singular-slice input [0,0],[1,2],[1,3],[3,4], or the Kashiwara–Saito example in GL₁₆, [-2,-1],[-2,-1],[-1,1],[-1,1],[0,0],[0,0],[1,2],[1,2], whose packet contains two representations.
Arthur Packets - allows you to inspect the $A$ -packet of a given $A$ -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, respectively, in the paper Construction of local A-packets by Hiraku Atobe. Also try the input (51,31), (31,45), (13,5) and compare it with Section 4.4 of loc. cit.
Extended multisegment inspector - allows you to inspect a given extended multisegment. You can see the representation this extended multisegment defines, the $A$ -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.
ABV Packets for G₂ computes unramified and dihedral packets for split $G_2(F)$ , with LLC enhancements, microlocal characters, and Aubert duals. Try the closed cubic packet with a rank-two member, the long-root dihedral Arthur packet, or the short-root dihedral packet with disconnected centralizer.