Seminar in Representation Theory
From Frieze Patterns to Root Systems of Nichols Algebras and Lie Superalgebras
2026/07/27 (Mon.) 10:00~11:30
- Date : 2026/07/27 (Mon.) 10:00~11:30
- Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
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Speaker : Shunsuke Hirota (Kyoto University)
- Organizer : Chun-Ju Lai (AS)
- Abstract : Conway–Coxeter frieze patterns are closely related to polygon triangulations. In rank two, the root systems of types $(A_2)$, $(B_2)$, and $(G_2)$ can be realized through frieze patterns associated with a triangle, quadrilateral, and hexagon.
This viewpoint was developed by Heckenberger and collaborators into a generalized theory of root systems allowing different choices of simple roots, leading to the classification of Nichols algebras of diagonal type and closely related to Kac's classification of basic classical Lie superalgebras.
Motivated by this framework, I will discuss root systems and representation theory of general linear Lie superalgebras, focusing on BGG resolutions, principal (W)-superalgebras, and super Kazhdan–Lusztig polynomials from the perspective of odd reflections.
