## Geometry and Topology

•  Anup Poudel, Ohio State
•  A comparison between $SL_n$ spider categories.
•  03/21/2023
•  2:00 PM - 3:00 PM
•  C304 Wells Hall
•  Vijay B Higgins (higgi231@msu.edu)

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.

## Contact

Department of Mathematics
Michigan State University
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C212 Wells Hall
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Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science