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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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148 [QSMS Symplectic topology seminar-20240514] Computing Fukaya categories: Techniques and Examples qsms 2024.05.10 13730
147 [QSMS Symplectic topology seminar-20240507]  Introduction to triangulated persistence categories qsms 2024.05.10 14073
146 [QSMS Monthly Seminar 2024-04-12] Local systems and finite group symmetry in Floer theory / Calabi-Yau structures on Rabinowitz Fukaya categories qsms 2024.04.12 13288
145 [QSMS Monthly Seminar 2024-03-22] Lifting problem for universal quadratic forms / Poincare duality in Rabinowitz Floer homology qsms 2024.03.22 13195
144 [SNU Topology seminar 2024-03-20] Topology of singularities of complex hypersurfaces / The monodromy conjecture for simplicial nondegenerate singularities qsms 2024.03.05 12907
143 [QSMS Representation theory seminar 2024-03-29] Quantum Grothendieck rings of Hernandez-Leclerc Categories qsms 2024.03.05 14033
142 [QSMS Representation theory seminar 2024-01-31] Kostant’s problem for Whittaker modules over Lie superalgebras qsms 2024.01.18 15228
141 [QSMS-BK21 symplectic semiar] Part 4 (23' Aug 18 ~) qsms 2023.12.27 19018
140 [QSMS Representation theory seminar 2023-12-28] Generalized polynomial functors qsms 2023.12.15 19085
139 [QSMS Monthly Seminar 2023-12-14] Simple singularity and their friends qsms 2023.12.14 14296
138 [QSMS Seminar 2023-12-13] A user’s guide to Schubert calculus of Lagrangian Grassmannians qsms 2023.11.27 18417
137 [QSMS Monthly Seminar 2023-11-11] Cluster structures on polygon spaces / From classical to quantum integrability qsms 2023.11.10 17488
136 [QSMS Symplectic geometry seminar 2023-10-24] Linear bounds on rho-invariants and simplicial complexity of manifolds qsms 2023.10.24 17754
» [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 17414
134 [KMS Specical Conference with 2022 Fields Medalists] Related talks qsms 2023.10.11 18307
133 [QSMS Symplectic geometry seminar 2023-10-17, 18] New approaches to discovering symplectic non-convexity / Banach-Mazur distances in symplectic and contact geometry qsms 2023.10.10 17427
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