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일정시작 2024-10-18
일정종료 2024-10-18
배경색상 #036eb7

2024년 10월 QSMS  Monthly Seminar

 

  • Date:   Oct 18th (Fri) 14:00 ~ 17:00
  • Place:  27-220 
  • Contents:

 

Speaker:  박의용 (오후2시)

Title:  Braid group actions on Grassmannians and extended crystals of type A

Abstract: Let $\sigma_i$ be the braid actions on infinite Grassmannian cluster algebras induced from Fraser’s braid group actions. Let $T_i$ be the braid group actions on (quantum) Grothendieck rings of Hernandez-Leclerc category $C^0_g$ of affine type $A$, and $R_i$ the braid group actions on the corresponding extended crystals. In this talk, I will talk about three braid group actions $\sigma_i$, $T_i$, and $R_i$ and show that they coincide. This is a joint work with Jian-rong Li.  

 

Speaker: 김영훈 (오후4시)

Title:  Modules of degenerate quantum groups for $P$-partition generating functions
Abstract:  Given a poset $P$ on $\{1, 2, \ldots, n\}$, a $P$-partition is an order-preserving map from $P$ to $\mathbb{Z}_{>0}$. The generating functions of $P$-partitions played a significant role in the development of quasisymmetric functions. The degenerate quantum group $\mathcal{U}_0(\mathfrak{gl}_N)$ is the $q=0$ specialization of the quantum group $\mathcal{U}_q(\mathfrak{gl}_N)$, introduced by Dipper and Donkin. In 1999, Krob and Thibon established a connection between quasisymmetric functions and polynomial $\mathcal{U}_0(\mathfrak{gl}_N)$-modules by defining the characters of these modules. In this talk, we study $P$-partitions and $\mathcal{U}_0(\mathfrak{gl}_N)$-modules. We then construct $\mathcal{U}_0(\mathfrak{gl}_N)$-modules, each of which has a basis consisting of $P$-partitions.

 

 

 


List of Articles
No. Subject Author Date Views
Notice QSMS Mailing List Registration qsms 2021.09.09 37491
162 weekplan_672_2020 secret qsms 2020.11.18 0
161 [QSMS Representation theory seminar-20241202] On finite-dimensional representations of quantum affine superalgebras of type A qsms 2024.11.23 78
160 [QSMS Symplectic geometry seminar-20240812] Exact Lagrangian tori in symplectic Milnor fibers constructed with fillings qsms 2024.08.10 298
159 [QSMS Monthly Seminar 2024-09-20] Braid varieties and cluster algebras / Symplectic geometry of Markov-type Diophantine equations qsms 2024.09.20 302
158 [QSMS Monthly Seminar 2024-11-15] Toric degenerations from Newton-Okounkov bodies / Flat F-manifolds for smooth projective complete intersection varieties qsms 2024.11.15 323
157 [QSMS Symplectic geometry seminar-20240812] Quantitative Floer theory and coefficients qsms 2024.08.03 395
156 [QSMS Symplectic geometry seminar-20240822] Outer symplectic billiard qsms 2024.08.22 449
155 [QSMS Representation theory seminar-20241122, 20241129] W-algebras and Quantum affine algebras qsms 2024.10.28 452
154 [QSMS Symplectic geometry seminar-20241105] 3d mirror symmetry I, II qsms2 2024.10.29 453
» [QSMS Monthly Seminar 2024-10-18] Braid group actions on Grassmannians and extended crystals of type A / Modules of degenerate quantum groups for $P$-partition generating functions qsms 2024.10.18 467
152 [QSMS Symplectic geometry seminar-20240805] Donaldson divisors and spectral invariants qsms 2024.08.03 531
151 [SNU Topology seminar 2024-03-20] Topology of singularities of complex hypersurfaces / The monodromy conjecture for simplicial nondegenerate singularities qsms 2024.03.05 13773
150 [QSMS Monthly Seminar 2024-03-22] Lifting problem for universal quadratic forms / Poincare duality in Rabinowitz Floer homology qsms 2024.03.22 13999
149 [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 14170
148 [QSMS Symplectic topology seminar-20240514] Computing Fukaya categories: Techniques and Examples qsms 2024.05.10 14568
147 [QSMS Monthly Seminar 2024-05-24] Cuspidal subgroups and rational torsion subgroups / Free subgroups generated by Dehn twists and its categorification qsms 2024.05.24 14590
146 [QSMS Representation theory seminar 2024-03-29] Quantum Grothendieck rings of Hernandez-Leclerc Categories qsms 2024.03.05 14743
145 [QSMS Seminar 2024-06-05] Curves, line bundles and Fourier transform qsms 2024.06.02 14772
144 [QSMS Symplectic topology seminar-20240507]  Introduction to triangulated persistence categories qsms 2024.05.10 14896
143 [QSMS Monthly Seminar 2023-12-14] Simple singularity and their friends qsms 2023.12.14 15224
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