Representations and Lie Theory SeminarAutumn 2023
Time: Tuesdays 11.30-12.30
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| TIME | SPEAKER | TITLE |
| September 12 | Jake Huryn | Some methods for descent of base field |
| September 26 | Ivo Herzog | Coherent Functors in Representation Theory |
| October 6 (Friday, 5PM, CH240) |
Oleksandr Tsymbaliuk | BGG-type relations for transfer matrices of rational spin chains and the shifted Yangians |
| October 10 | No Seminar - Fall break week! | |
| October 24 | Staff | R-matrices |
| October 31 | Staff | Yangians and meromorphic R-matrices |
| November 7 | ||
| November 14 | Cemile Kurkoglu | Duality in category O and locally analytic representations |
| November 21 | No seminar - Thanksgiving week! | |
| November 28 | ||
| December 5 |
September 12. Let $K|k$ be a field extension in characteristic 0. If the character of an irreducible representation $\rho$ over $K$ of an abstract group takes values in $k$, one can ask whether $\rho$ is itself defined over $k$. In this talk I will describe some cases when this can or cannot be done and give some applications to arithmetic geometry.
September 26. After a brief introduction to Auslander's theory of coherent functor and their role in the proof of existence for almost split (Auslander-Reiten) sequences. I will explain how the category of coherent functors is used to study finite-dimensional representations of a semisimple Lie algebra.
October 6. In this talk, I will discuss: (1) the new BGG-type resolutions of finite dimensional representations of simple Lie algebras that lead to BGG-relations expressing finite-dimensional transfer matrices via infinite-dimensional ones, (2) the factorization of infinite-dimensional ones into the product of two Q-operators, (3) the construction of a large family of rational Lax matrices from antidominantly shifted Yangians. This talk is based on the joint works with R.Frassek, I. Karpov, and V.Pestun.
October 24. In this introductory talk, I will explain what is the Yang-Baxter equation, and how the theory of quantum groups gives rise to its solutions, i.e., R-matrices.
October 31. Yangians were introduced by Drinfeld in 1985, as a family of quantum groups whose representations carry rational solutions to the Yang-Baxter equation (i.e., rational R-matrices). In this talk I will present a novel technique to compute these R-matrices, discovered in our joint works with Valerio Toledano Laredo, Curtis Wendlandt and Andrea Appel. Time permitting, I will present a conjecture relating our construction to the stable basis map of Maulik-Okounkov.
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