Non-crossing partitions and webs

Stephan Pfannerer (U Waterloo)

Feb 21. 2025, 11:15 — 11:45

Webs give a diagrammatic calculus for spaces of SL(r)-tensor invariants, but intrinsic characterizations of web bases are only known in certain cases.

In recent joint work with Christian Gaetz, Oiver Pechenik, Jessica Striker and Joshua Swanson we have introduced hourglass plabic graphs as a new avatar of webs to give the first rotation invariant SL(4)-web bases.

In this talk I will discuss a construction that produces an hourglass plabic graph from a non-crossing partition and its Kreweras complement, which recovers Chris Fraser's rotation-invariant web basis for Plücker degree two representations of arbitrary SL(r).

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability (Workshop)
Organizer(s):
Adrian Celestino Rodriguez (TU Graz)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
James Mingo (Queen's U, Kingston)
Martin Rubey (TU Vienna)
Eleni Tzanaki (U of Crete)
Yannic Vargas (CUNEF U, Madrid)