KCL2023.07

It is a triannual (three-times-a-year) seminar organized by academic genealogy from Professor Dongsu Kim in KAIST Combinatorics Laboratory, which KCL stands for. The aim of this seminar is to bring together active combinatorialists to discuss recent and prospective advances in algebraic and enumerative combinatorics and related areas. The style of talk tends to be less formal.

Program

• July 10 (Monday)

  • 13:50 - 14:00 Registration

  • 14:00 - 15:00 Invited Talk

    • Speaker Ae Ja Yee

    • Title The Rogers–Ramanujan Identities and Ariki–Koike Algebras

    • Abstract In 2000, Ariki and Mathas showed that the simple modules of the Ariki–Koike algebras ℋℂ, v; Q1, …, Qm(G(m,1,n)) (when the parameters are roots of unity and v ≠ 1) are labeled by the so-called Kleshchev multipartitions. This together with Ariki’s categorification theorem enabled Ariki and Mathas to obtain the generating function for the number of Kleshchev multipartitions by making use of the Weyl–Kac character formula. In this talk, I will revisit this generating function for v = Q1 = ⋯ = Qa =  − 1, Qa + 1 = ⋯ = Qm = 1. This case is particularly interesting, for the corresponding Kleshchev multipartitions have a very close connection to the Rogers–Ramanujan identities. I will discuss an analytic proof of this generating function.
      The second objective of this talk is to count the number of simple modules of the Ariki–Koike algebra in a fixed block. It is known that the simple modules of the Ariki–Koike algebras in a fixed block are labeled by the Kleshchev multiparitions with a fixed partition residue statistic. This partition statistic was also studied in the works of Berkovich, Garvan, and Uncu. Employing their results, we can get two bivariate generating function identities for m = 2. I will also discuss these identities.
      This talk is based on joint work with S. Chern, Z. Li, D. Stanton, and T. Xue.

  • 15:00 - 15:20 Coffee Break

  • 15:20 - 17:00 Lightning Talks (Up to 10 minutes each for all participants)

  • 17:00 - 20:00 Dinner (Mad for Garlic, Gwanghwamun D Tower)

Organizer

• Seunghyun Seo, Kangwon National University