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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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143 [SNU Topology seminar 2024-03-20] Topology of singularities of complex hypersurfaces / The monodromy conjecture for simplicial nondegenerate singularities qsms 2024.03.05 2734
142 [QSMS Representation theory seminar 2024-03-29] Quantum Grothendieck rings of Hernandez-Leclerc Categories qsms 2024.03.05 2796
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140 [QSMS Monthly Seminar 2023-12-14] Simple singularity and their friends qsms 2023.12.14 2880
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136 [SNU Number Theory Seminar 2022-04-15] A note on non-ordinary primes for some genus-zero arithmetic groups qsms 2022.04.12 2951
135 [QSMS Seminar 2023-05-17] Affinizations, R-matrices and reflection functors qsms 2023.05.04 2962
134 [SNU Number Theory Seminar 2022-05-13] A singular function containing all Lagrange numbers less than three qsms 2022.04.12 2973
133 [QSMS Seminar 2022-10-11] (q,t)-Cartan matrix and representation theories related to the specializations of the matrix file qsms 2022.09.18 2974
132 [QSMS-BK21 symplectic semiar] Part 4 (23' Aug 18 ~) qsms 2023.12.27 2975
131 [QSMS-BK21 Symplectic Geometry Seminar 2022-12-09] Introduction to Floer Homotopy: Formal Groups and Complex Cobordism qsms 2022.11.28 2976
130 [QSMS Seminar 2022.04.19] Universal objects in vertex algebra theory qsms 2022.04.07 2977
129 [QSMS Seminar 2022-10-25] Rational liftings and gRSK qsms 2022.10.08 2977
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