?

단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
?

단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
Extra Form
일정시작 2022-08-31
일정종료 2022-08-31
배경색상 #77CC00
  • Date :  2022-08-31 (Wed) 11:00 ~ 12:00
  • Place :  129-406 (SNU)

  • Speaker :  김명호 (경희대학교)
  • Title :  Localization of the category of modules over quiver Hecke algebras
  • Abstract :

For each w in the Weyl group, there is a subcategory C_w of the category of finite-dimensional modules over the quiver Hecke algebra, which categorifies the (quantum) coordinate ring of the unipotent subgroup N(w). More precisely, there exists a ring isomorphism from the coordinate ring C[N(w)] to the Grothendieck ring of C_w  and it sends a cluster monomial to an isomorphism class of simple modules in C_w. It is known that the localization of the C[N(w)] via the frozen variables is isomorphic to the coordinate ring C[N_w] of the unipotent cell N_w. 
 We develop a localization process of a k-linear abelian monoidal category via a family of simple objects and apply it to the case of category C_w with the simple modules corresponding to frozen variables.  It turns out that the Grothendieck ring of the localization of C_w is isomorphic to the coordinate ring C[N_w] of the unipotent cell and it respects cluster algebra structures. A remarkable fact is that any object in the localization of C_w admits a left dual and a right dual. This corresponds to an algebra automorphism on C[N_w], so called the (quantum) twist map.

 

 

 

 


 


List of Articles
번호 제목 글쓴이 날짜 조회 수
공지 QSMS Mailing List Registration qsms 2021.09.09 13286
70 [QSMS Symplectic topology seminar-20240507]  Introduction to triangulated persistence categories qsms 2024.05.10 204
69 [QSMS Symplectic topology seminar-20230828] From Babylonian lunar observations to global surfaces of section qsms 2023.08.21 3870
68 [QSMS Symplectic topology seminar 20230817] Symplectic Torelli classes of positive entropy qsms 2023.08.14 3814
67 [QSMS Symplectic topology seminar 20230811, 0817] Spectral numbers in Tate Rabinowitz Floer Homology qsms 2023.08.04 3829
66 [QSMS Symplectic geometry seminar 2023-10-24] Linear bounds on rho-invariants and simplicial complexity of manifolds qsms 2023.10.24 3821
65 [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 3666
64 [QSMS Seminar 2024-06-05] Curves, line bundles and Fourier transform qsms 2024.06.02 178
63 [QSMS Seminar 2023-12-13] A user’s guide to Schubert calculus of Lagrangian Grassmannians qsms 2023.11.27 3767
62 [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 3903
61 [QSMS Seminar 2023-05-17] Affinizations, R-matrices and reflection functors qsms 2023.05.04 3370
60 [QSMS Seminar 20220721] Finding ALL solutions qsms 2022.07.14 3996
59 [QSMS Seminar 2022.04.19] Universal objects in vertex algebra theory qsms 2022.04.07 3435
58 [QSMS Seminar 2022.04.05] Trialities of W-algebras qsms 2022.02.15 3397
57 [QSMS Seminar 2022.03.04 (시간변경)] Introduction to Supersymmetric Field Theories qsms 2022.02.15 3631
56 [QSMS Seminar 2022-12-2] N=2 supersymmetric W algebras from Hamiltonian reduction qsms 2022.11.25 3288
55 [QSMS Seminar 2022-10-25] Rational liftings and gRSK qsms 2022.10.08 3374
54 [QSMS Seminar 2022-10-11] (q,t)-Cartan matrix and representation theories related to the specializations of the matrix file qsms 2022.09.18 3353
53 [QSMS Seminar 2022-09-27] Categories of Whittaker Modules over Lie superalgebras and Categorification of Fock Spaces qsms 2022.09.20 3387
» [QSMS Seminar 2022-08-31] Localization of the category of modules over quiver Hecke algebras qsms 2022.08.25 3496
51 [QSMS Seminar 2022-08-24] Vector bundles and representation theory on a curve qsms 2022.08.13 3426
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8