Extra Form
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.

 

 

 

 


List of Articles
번호 제목 글쓴이 날짜 조회 수
공지 QSMS Mailing List Registration qsms 2021.09.09 2461
142 [QSMS Representation theory seminar 2024-01-31] Kostant’s problem for Whittaker modules over Lie superalgebras qsms 2024.01.18 201
141 [QSMS-BK21 symplectic semiar] Part 4 (23' Aug 18 ~) qsms 2023.12.27 281
140 [QSMS Representation theory seminar 2023-12-28] Generalized polynomial functors qsms 2023.12.15 305
139 [QSMS Monthly Seminar 2023-12-14] Simple singularity and their friends qsms 2023.12.14 306
138 [QSMS Seminar 2023-12-13] A user’s guide to Schubert calculus of Lagrangian Grassmannians qsms 2023.11.27 397
137 [QSMS Monthly Seminar 2023-11-11] Cluster structures on polygon spaces / From classical to quantum integrability qsms 2023.11.10 376
136 [QSMS Symplectic geometry seminar 2023-10-24] Linear bounds on rho-invariants and simplicial complexity of manifolds qsms 2023.10.24 406
» [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 2023.10.13 372
134 [KMS Specical Conference with 2022 Fields Medalists] Related talks qsms 2023.10.11 398
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 2023.10.10 359
132 [QSMS Representation theory seminar - 2023-10-17] A Data-Scientific Approach to Representation Theory: Case Study of Kronecker Coefficients qsms 2023.09.27 381
131 [QSMS Monthly Seminar] Quiver Hecke algebras and open Richardson varieties qsms 2023.09.22 447
130 [QSMS Seminar 2023-10-06, 11-03] Algebraic group analogues of the Slodowy slices and the structure of the set of conjugacy classes in algebraic groups / Poisson q-W-algebras qsms 2023.09.11 524
129 [QSMS Symplectic topology seminar-20230828] From Babylonian lunar observations to global surfaces of section qsms 2023.08.21 519
128 [QSMS Symplectic topology seminar 20230817] Symplectic Torelli classes of positive entropy qsms 2023.08.14 515
127 [QSMS Symplectic topology seminar 20230811, 0817] Spectral numbers in Tate Rabinowitz Floer Homology qsms 2023.08.04 579
126 [QSMS-BK21 Symplectic Seminar 28 July] Nonexistence of Exact K(G,1) Lagrangians in Milnor Fibers of Weighted Homogeneous Polynomials / Associative Yang-Baxter Equation and Fukaya Categories qsms 2023.07.17 520
125 [QSMS-BK21 Symplectic Seminar 14 July] Introduction to 3D Mirror Symmetry, from a Symplectic Viewpoint / Orbifolding Lagrangian Floer Cohomology qsms 2023.07.12 555
124 [SNU Number Theory Seminar 30 June] Do Tropical Markov Cubics dream of Hyperbolic Origami? qsms 2023.06.26 669
123 [QSMS-BK21 Symplectic Seminar 30 June] Matrix Factorizations qsms 2023.06.26 494
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8