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IRT seminar: Alexander Tsymbaliuk: Lyndon words and quantum groups

Event Type
Integrability and Representation Theory seminar
241 Altgeld Hall
Mar 2, 2023   12:30 pm  
Alexander Tsymbaliuk (Purdue)
Originating Calendar
Integrability & Representation Theory (IRT) Seminar
Lyndon words and quantum groups

Classical q-shuffle 
algebras provide combinatorial models for the positive half U_q(n) of a finite quantum group. 
We define a loop version of this construction, yielding a combinatorial model for the positive half U_q(Ln) of a quantum loop group. In particular, we construct a PBW basis of U_q(Ln) indexed by standard Lyndon words, generalizing the work of Lalonde-Ram, Leclerc and Rosso in the U_q(n) case. We also connect this to Enriquez' degeneration A of the elliptic algebras of Feigin-Odesskii, proving a conjecture that describes the image of the embedding U_q(Ln) -> A in terms of pole and wheel conditions. This is a joint work with Andrei Negut.
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