Representation Theory and its Combinatorial Aspects

October 28 (Mon), 2019 - Octorber 31(Thu), 2019

Research Institute for Mathematical Sciences, Kyoto University

Representation Theory and its Combinatorial Aspects

These days the representation theory of the algebraic groups, quantum groups, Iwahori Heck algebra and related algebras plays important roles in mathematics and theoretical physics. The study of the problems in the representation theory of these algebras is expected to have significant progress and rich application by using tools of combinatorial objects such as Young diagrams, symmetric functions, crystal bases, quivers and the graph theory. This Symposia focus on giving the NICE combinatorial objects corresponding to the representation theory and study of the property of those objects such as dimensions, characters, branching rules and so on. We are especially interested in

  1. Study of the finite dimensional representations of affine quantum groups and their crystal bases
  2. Combinatorial descriptions of Weyl groups, complex reflection groups, and the modular representations of the Hecke algebras
  3. Algebraic varieties, Grassmaniann manifolds, Schubert polynomials
  4. Application of the combinatorial property of the symmetric functions to the representation theory, especially realization of the representations of affine Lie algebras in polynomial rings
  5. Combinatorial meanings of the integral values on the classical compact Lie groups
  6. Application of the representation theory and symmetric functions to enumerative combinatorics
  7. Enumeration of alternating sign matrices, plane partitions, and tilings
  8. Random matrices and the integrable systems

Abstract of the talks

You can download a PDF file of the abstracts of the talks in this Symposia.


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