Ruhr-University Bochum and Technical University of Munich
Tuesdays 12-14 (CET)
Organized by: Deniz Kus (TUM), Markus Reineke (RUB)
The Ruhr University Bochum and the Technical University of Munich jointly organize an Oberseminar on Representation Theory. The seminar serves as a platform to present and discuss recent developments in algebra, representation theory, and related fields.
Talks are scheduled on Tuesdays, 12:15–13:45 (CET) and typically last about 60 minutes including discussion. Most talks take place online; only a few will be held on-site and streamed.
If you are interested in attending, please contact one of the organizers to receive the link.
20.10.26: Alice Dell'Arciprete (RUB)
Title: Characters, Cartan invariants and Ext-quiver of the Mantaci-Reutenauer algebra
Abstract: The Mantaci-Reutenauer algebra arises as simultaneous generalisation of the descent algebra of the symmetric group and the descent algebra of the hyperoctaedral group. There are many open questions about the representation theory of the Mantaci Reutenauer algebra. In this talk, we will give a combinatorial characterization of the characters of these algebras and present some conjectures about the decomposition numbers and the Ext-quiver of these algebras. This is joint work with Patty Commins.
27.10.26: details via email
03.11.26: Élie Casbi (University of Vienna)
Title: Representation theory of quantum affine algebras via tensor products of modules over hereditary algebras
Abstract: We introduce new families of monoidal structures suited to categorifying important invariants arising in the representation theory of quantum affine algebras and in the theory of cluster algebras. Our framework builds on Auslander–Reiten theory and higher homological algebra; namely, for each finite acyclic quiver Q, we construct a monoidal category R_Q whose indecomposable objects are tensor products of modules over the path algebra of Q. We show that to each indecomposable object X in R_Q corresponds a (unique up to homotopy) chain complex C(X) satisfying remarkable homological properties. These complexes are constructed using some iterated mapping cone procedure, which yields a collection of distinguished triangles in the bounded homotopy category of R_Q. We then prove that in the case where Q is a Dynkin quiver, the Euler characteristics of (the image under a suitable functor of) C(X) can be identified with the (truncated) q-character of a standard module over the quantum affine algebra U_q(\hat{g_Q)). We also show that the above mentioned distinguished triangles categorify certain exchange relations in the finite type cluster algebra A_Q. If time allows, we will discuss perspectives towards monoidal categorifications of more general cluster structures.
10.11.26: Divya Setia (Polish Academy of Sciences IMPAN)
Title: Tensor decomposition of Demazure crystals
Abstract: The study of Demazure crystals has been a central topic in representation theory for several years. The talk will be based on exploring the decomposition problem for the tensor product of Demazure crystals. In general, it is not necessary that the tensor product of Demazure crystals decomposes as a disjoint union of Demazure crystals. In this talk, I will discuss the necessary and sufficient conditions obtained in our recent work for the decomposition of the tensor product of Demazure crystals as a disjoint union of Demazure crystals for symmetrizable Kac-Moody Lie algebras. Theseresults also provide a partial solution to the key positivity problem.
17.11.26: Igor Makhlin (TU Berlin)
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24.11.26: details via email
01.12.26: details via email
08.12.26: details via email
15.12.26: details via email
12.01.27: Stefan Kolb (Newcastle University)
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19.01.27 : Huafeng Zhang (Université de Lille)
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26.01.27: details via email