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This is an informal learning seminar on quantum groups and related topics, mainly held at Tokyo Institute of Technology.
Please feel free to contact me (Hironori OYA) if you would like to participate. Seminar talks are given mainly in Japanese, while some notes are written in English. |
| Date | Topic | Main Reference |
| Jul. 19 | Baxter polynomiality and Frenkel-Reshetikhin conjecture [Hironori Oya] | [FH] |
| Jun. 14 | The operator $T_i(z)$ and its eigenvalues on finite dimensional modules [Hironori Oya] | [FH], [D] |
| May 23 | Definition of twisted transfer matrices for modules in $\mathcal{O}^{\ast}$ (continued), Commutativity of twisted transfer matrices [Hironori Oya] | [FH], [Lbook] |
| May 15 | Definition of twisted transfer matrices for modules in $\mathcal{O}^{\ast}$ [Hironori Oya] | [FH], [Lbook] |
| Apr. 19 | Simplicity of tensor products of prefundamental modules [Hironori Oya] | [FH] |
| Apr. 05 | Generalized Baxter's relations in the categories $\mathcal{O}$ and $\mathcal{O}^{\ast}$ [Hironori Oya] | [FH] |
| Mar. 22 | Frenkel-Reshetikhin conjecture, Review of the category $\mathcal{O}$ for Borel subalgebras [Hironori Oya] | [FH] |
| Date | Topic | Main Reference |
| Jan. 27 | Asymptotic representations III [Hironori Oya] | [HJ] |
| Jan. 20 | Asymptotic representations II [Hironori Oya] | [HJ] |
| Jan. 06 | Asymptotic representations I [Hironori Oya] | [HJ], [H] |
| Dec. 23 | Category $\mathcal{O}$ for Borel subalgebras of quantum loop algebras II [Hironori Oya] | [HJ] |
| Dec. 09 | Category $\mathcal{O}$ for Borel subalgebras of quantum loop algebras I [Hironori Oya] | [HJ] |
| [D] | I. Damiani, La $R$-matrice pour les algèbres quantiques de type affine non tordu, Ann. Sci. École Norm. Sup. (4) 31 (1998), no.4, 493--523. |
| [FH] | E. Frenkel and D. Hernandez, Baxter's relations and spectra of quantum integrable models, Duke Math. J. 164 (2015), no. 12, 2407--2460. |
| [H] | D. Hernandez, Simple tensor products, Invent. Math. 181 (2010), no. 3, 649--675. |
| [HJ] | D. Hernandez and M. Jimbo, Asymptotic representations and Drinfeld rational fractions, Compos. Math. 148 (2012), no. 5, 1593--1623. |
| [Lbook] | G. Lusztig, Introduction to quantum groups, Reprint of the 1994 edition, Mod. Birkhäuser Class. Birkhäuser/Springer, New York, 2010. xiv+346 pp. |
Last updated on July 23, 2024.