A comparison between SL_n spider categories

Geometry Topology Seminar
Monday, March 27, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Anup Poudel – Ohio State – poudel.33@osu.eduhttps://sites.google.com/view/anup-poudel/home
Wade Bloomquist

In this talk, we will explore and make comparisons between various models that exist for spherical tensor categories associated to the category of representations of the quantum group U_q(SL_n). In particular, we will discuss the combinatorial model of Murakami-Ohtsuki-Yamada (MOY), the n-valent ribbon model of Sikora and the trivalent spider category of Cautis-Kamnitzer-Morrison (CKM). We conclude by showing that the full subcategory of the spider category from CKM, whose objects are monoidally generated by the standard representation and its dual, is equivalent as a spherical braided category to Sikora's quotient category. This proves a conjecture of Le and Sikora and also answers a question from Morrison's Ph.D. thesis.