Titles and Abstracts :

1. Speaker : Kwon, Jaehoon (Sungkyunkwan University)

Title: "Super duality and crystal bases"

Abstract:
We introduce a semisimple tensor category of modules over an quantum orthosymplectic superalgebra. It is a natural counterpart of the category of finitely dominated integrable modules over the quantum classical (super) algebra of type $B_{m+n}$, $C_{m+n}$, $D_{m+n}$ or $B(0,m+n)$ from a viewpoint of super duality. We show that a highest weight module in this category has a unique crystal base when it corresponds to a highest weight module of type $B_{m+n}$, $C_{m+n}$ or $B(0,m+n)$ under super duality. We also give a combinatorial model for these crystals, which can be viewed as a natural super analogue of Kashiwara-Nakashima tableaux of classical type $B$ and $C$.

2. Speaker : Kim, Myungho (KIAS)

Title: "Symmetric quiver Hecke algebras and $R$-matrices"

Abstract:
Let $U'_q(g)$ be a quantum affine algebra. For a given family of pairs consisting of simple $U'_q(g)$-modules and nonzero scalars, we construct a functor from the category of modules over a symmetric quiver Hecke algebras to the category of $U'_q(g)$-modules. The functor and corresponding symmetric quiver Hecke algebras are determined by the distribution of poles of normalized $R$-matrices. In this talk, we will review the above construction and provide an application of it.

3. Speaker : Park, Euiyong (University of Seoul)

Title: "Representation type of finite quiver Hecke algebras"

Abstract:
In this talk, we review the categorification for quantum groups using quiver Hecke algebra, and explain my recent work on finquiver Hecke algebras $R^\Lambda_0(\beta)$ with Susumu Ariki at Osaka University. The algebra $R^\Lambda_0(\beta)$ can be understood as an analogue of Iwahori-Hecke algebras associated with the symmetric group. We explain a dimension formula for the algebra $R^\Lambda_0(\beta)$ of type $A_{2\ell}^{(2)}$ using Fock space theory, and give a simple criterion to tell the representation type. The criterion is a natural generalization of Erdmann and Nakano's for the Iwahori-Hecke algebras. This talk is based on arXiv:1208.0889.

4. Speaker : Cho, Soojin (Ajou University)

Title: "A Shifted Littlewood-Richardson Rule"

Abstract:
A new description of shifted Littlewood-Richardson rule (Littlewood-Richardson rule for Schur P-functions) is given in terms of plactic monoid elements. We consider the problem to define plactic skew Schur P-functions; we explain the main difficulty on the problem and suggest a model of plactic skew Schur P-functions.

5. Speaker : Jonathan Axtell (Seoul National University)

Title: "Super Schur Functors"

Abstract:
We discuss super-analogues of the Schur and co-Schur functors defined by Akin, Buchsbaum and Weyman in their 1982 paper. In particular, we describe a standard basis in terms on $(m,n)$-hook tableaux and give Cauchy decomposition formulas for super Schur functors.

5. Speaker : Yoo, Hwanchul (KIAS)

Title: "Diagram Specht Modules, Symmetric Functions, and Matching Ensemble Polytopes"

Abstract:
In this talk, the diagram Specht modules and related objects are going to be discussed. In particular, we introduce matching ensemble polytope and the conjecture on its volume. We will discuss several evidences to the conjecture, including the toric Specht modules, cylindric Schur functions, diagrams of permutations and Stanley symmetric functions.