Combinatorial Representation Theory Afternoon

Friday, February 17, 2017

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

The Combinatorial Representation Theory Afternoon takes place in room f435 (Stahlbausaal) in the main building of Leibniz Universität Hannover, the Welfenschloss; coffee breaks are in room a410.

Christian Stump (FU Berlin)
Generalized Cambrian lattices via spherical Artin monoids, noncrossing partitions, cluster complexes, and hereditary algebras

In this talk, I will present and discuss four a priori independent definitions of generalized Cambrian lattices, and then conclude that all these definitions coincide. These definitions are (1) sortable elements in spherical Artin groups with poset structure inherited from the weak order, (2) generalized noncrossing partitions under componentwise refinement, (3) generalized cluster complexes under positive flips, and (4) mutations in the generalized cluster category as defined by Buan-Reiten-Thomas in "From m-clusters to m-noncrossing partitions via exceptional sequences". To connect all these objects and show that the defined order coincide, I will present a common recursive structure of all these objects.
This is joint work with Hugh Thomas and Nathan Williams.
Jørn B. Olsson (University of Copenhagen)
Odd-dimensional representations of finite symmetric groups

The talk is primarily concerned with correspondences of odd-degree characters of the symmetric groups and some of their natural subgroups, which can be described easily by restriction of characters, degrees and multiplicities. (Joint work with I.M. Isaacs, Gabriel Navarro and Pham Huu Tiep.)
Eugenio Giannelli (University of Cambridge)
Character correspondences of type McKay for finite symmetric and general linear groups at the prime 3

Let G be the symmetric group or the general linear group. In this talk I will present some recent work on the McKay Conjecture at the prime 3. In particular, I will describe a canonical bijection between the irreducible characters of G of degree coprime to 3 and those of N_G(P), where P is a Sylow 3-subgroup of G. This is joint work with Joan Tent and Pham Tiep.

Christine Bessenrodt
Last update: Feb 17, 2017