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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 37511
42 [QSMS Monthly Seminar]Introduction to modular curves and modular forms qsms 2020.12.02 19053
41 [QSMS Monthly Seminar] Yokonuma Hecke algebras and invariants of framed links qsms 2022.05.27 17575
40 [QSMS Monthly Seminar] Symmetric functions and super duality qsms 2021.05.28 18678
39 [QSMS Monthly Seminar] Smoothing of Fano varieties and mutations qsms 2021.09.23 18399
38 [QSMS Monthly Seminar] Recoverable lattices qsms 2021.05.07 18479
37 [QSMS Monthly Seminar] Quantum entanglement entropy in abelian arithmetic Chern-Simons theory qsms 2021.10.29 18096
36 [QSMS Monthly Seminar] Quantization of integrable differential difference equations qsms 2022.04.22 17799
35 [QSMS Monthly Seminar] Peterson conjecture via Lagrangian correspondences and wonderful compactifications qsms 2020.11.18 35883
34 [QSMS Monthly Seminar] Introduction to finite-dimensional representations of quantum affine algebras qsms 2021.12.03 17782
33 [QSMS Monthly Seminar] Introduction to cluster algebras (and monoidal categorification) qsms 2020.11.18 21082
32 [QSMS Monthly Seminar] Closed orbits and Beatty sequences qsms 2021.06.24 18643
31 [QSMS Monthly Seminar] Canonical basis qsms 2020.11.18 21889
30 [QSMS Monthly Seminar] A survey on symplectic fillings and Milnor fibers of a normal complex surface singularity qsms 2021.03.26 18839
29 [QSMS Monthly Seminar] The dimension of the kernel of an Eisenstein ideal qsms 2022.03.25 18020
28 [QSMS Monthly Seminar] Quiver Hecke algebras and open Richardson varieties qsms 2023.09.22 18126
27 [QSMS Monthly Seminar 2024-11-15] Toric degenerations from Newton-Okounkov bodies / Flat F-manifolds for smooth projective complete intersection varieties qsms 2024.11.15 366
» [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 2024.10.18 535
25 [QSMS Monthly Seminar 2024-09-20] Braid varieties and cluster algebras / Symplectic geometry of Markov-type Diophantine equations qsms 2024.09.20 305
24 [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 14627
23 [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 14175
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