`2021-04-14 16:15:00``2021-04-14 17:15:00``Quantum loop groups and shuffle algebras via Lyndon words``Speaker: Oleksandr Tsymbaliuk (Purdue University) Title: Quantum loop groups and shuffle algebras via Lyndon words Speaker's URL: https://www.math.purdue.edu/~otsymbal/ Abstract: 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. Joint work with Andrei Negut. URL associated with Seminar https://research.math.osu.edu/reps/``Online``OSU ASC Drupal 8``ascwebservices@osu.edu``America/New_York``public`

`2021-04-14 16:15:00``2021-04-14 17:15:00``Quantum loop groups and shuffle algebras via Lyndon words``Speaker: Oleksandr Tsymbaliuk (Purdue University) Title: Quantum loop groups and shuffle algebras via Lyndon words Speaker's URL: https://www.math.purdue.edu/~otsymbal/ Abstract: 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. Joint work with Andrei Negut. URL associated with Seminar https://research.math.osu.edu/reps/``Online``Department of Mathematics``math@osu.edu``America/New_York``public`**Speaker: **Oleksandr Tsymbaliuk (Purdue University)

**Title: **Quantum loop groups and shuffle algebras via Lyndon words

**Speaker's URL: **https://www.math.purdue.edu/~otsymbal/

**Abstract: **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. Joint work with Andrei Negut.

**URL associated with Seminar**

https://research.math.osu.edu/reps/