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Seminars

Seminar in Representation Theory

The ring of universal characters of type A and extremal weight crystals

2026/05/13 (Wed.) 15:30~16:30
  • Date : 2026/05/13 (Wed.) 15:30~16:30
  • Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
  • Speaker : Jae-hoon Kwon (Seoul National University)
  • Organizer : Chun-Ju Lai (AS)
  • Abstract : The ring of universal characters was introduced by Koike to explain the stability phenomenon appearing in the decomposition of tensor products of rational representations of complex general linear groups. There are several works to give a representation theoretic interpretation of it. In this talk, we give another one in terms of quantum groups. More precisely, we show that the ring of universal characters of type A can be realized as the Grothendieck ring of a non-semisimple category of representations of quantum groups of type $A_+\infty$, generated by extremal weight modules. We also describe the socle filtration of the tensor product of any two extremal weight modules. This is a joint work with Soo-Hong Lee.
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