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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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113 [QSMS-BK21 Toric Geometry Seminar] Moduli Space of Special Lagrangians in the Complement of an Anticanonical Divisor qsms 2022.04.12 18253
112 [QSMS 집중강연 Representation theory 2023-02-13] Mini-course on quantum symmetric pairs II qsms 2023.01.05 18261
111 [QSMS Seminar 14,16 Dec] A brief introduction to differential graded Lie algebras I, II qsms 2021.11.29 18270
110 [QSMS Seminar 2022-08-24] Vector bundles and representation theory on a curve qsms 2022.08.13 18288
109 [BK21-QSMS Toric Geometry Seminar] The Fredholm regularity of discs qsms 2022.03.14 18314
108 [Seminar 2021.05.14] On some results about non-holomorphic Jacobi forms qsms 2021.05.11 18321
107 [QSMS Seminar 2022-08-31] Localization of the category of modules over quiver Hecke algebras qsms 2022.08.25 18336
106 [Seminar 2021.05.18] The coherent-constructible correspondence for toric projective bundles qsms 2021.05.17 18366
105 [QSMS Monthly Seminar] Quantum entanglement entropy in abelian arithmetic Chern-Simons theory qsms 2021.10.29 18379
104 [SNU Number Theory Seminar 2022-11-04] Approximations with mod 2 congruence conditions qsms 2022.10.27 18383
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