Quantum loop groups and shuffle algebras via Lyndon words

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Oleksandr Tsymbaliuk
April 14, 2021
4:15PM - 5:15PM
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Online

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Add to Calendar 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
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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/

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