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일정시작 2023-10-13
배경색상 #036eb7

2023년 10월 QSMS  Monthly Seminar

 

  • Date:   Oct. 13th (Fri) 14:00 ~ 17:00
  • Place:  129-101 (SNU)
  • Contents:

 

Speaker:  박의용 (서울시립대)
Title:  Quantum Grothendieck rings of Hernandez-Leclerc categories

Abstract: Let $C_\ell$ be a Hernandez-Leclerc category of a quantum affine algebra, and let $\tilde{A}_q(\ell)$ be its quantum Grothendieck ring. The ring $\tilde{A}_q(\ell)$ has a cluster algebra structure. In particular, when it is of type A,  $\tilde{A}_q(\ell)$ can be understood as a deformation of the quotient ring of the coordinate ring of the Grassmannian. In this talk, I will talk about the structure of the ring $\tilde{A}_q(\ell)$ from the viewpoint of cluster algebras and explain recent progress on $\tilde{A}_q(\ell)$ including extended crystals and braid group actions.  

 

Speaker:  김영훈 (서울대)
Title:  Regular Schur labeled skew shape posets and their 0-Hecke modules
Abstract:  In 1972, Stanley proposed a conjecture that for a labeled finite poset $(P,\omega)$, the $(P,\omega)$-partition generating function is symmetric if and only if $(P,\omega)$ is isomorphic to a Schur labeled skew shape poset. If this conjecture holds, then for a weak Bruhat interval module $\mathsf{B}$ of the $0$-Hecke algebra, the quasisymmetric characteristic image of $\mathsf{B}$ is symmetric if and only if $\mathsf{B}$ is isomorphic to a $0$-Hecke module associated to a regular Schur labeled skew shape poset. In this talk, we investigate regular Schur labeled skew shape posets $P$ and their $0$-Hecke modules $\mathsf{M}_P$. First, we study the relationship between regular Schur labeled skew shape posets and left weak Bruhat intervals. Then, we give characterizations of regular Schur labeled skew shape posets. Using these characterizations, we provide a classification of $\mathsf{M}_P$'s up to module isomorphism and find a filtration of $\mathsf{M}_P$ which gives a $0$-Hecke module theoretic interpretation for the Littlewood-Richardson rule for Schur functions. This talk is based on joint work with So-Yeon Lee and Young-Tak Oh.

 

 

 

 


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» [QSMS Monthly Seminar 2023-10-13] Quantum Grothendieck rings of Hernandez-Leclerc categories / Regular Schur labeled skew shape posets and their 0-Hecke modules qsms 2023.10.13 3000
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16 [QSMS Monthly Seminar 2023-03-24] Rational points on abelian varieties qsms 2023.03.24 2936
15 [QSMS Monthly Seminar 2022-12-02] Extended crystal structures of Hernandez-Leclerc categories qsms 2022.12.02 3005
14 [QSMS Monthly Seminar 2022-10-28] Oscillator representations of quantum affine algebras   qsms 2022.10.30 2978
13 [QSMS Monthly Seminar 2022-09-30] Monotone Lagrangians via toric degenerations: algebraic approach qsms 2022.09.30 2996
12 [QSMS Mini-course] Pablo Portilla cuadrado (University of Lille) qsms 2022.07.04 3070
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9 [QSMS Geometry Seminar 2022-05-17, 19] Symplectic Criteria on Stratified Uniruledness of Affine Varieties and Applications qsms 2022.05.09 3060
8 [QSMS Geometry Seminar 2022-05-12] Tropical Lagrangian multi-sections and tropical locally free sheaves qsms 2022.05.07 3023
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