조회 수 14680 추천 수 0 댓글 0
?

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 2022-10-25
일정종료 2022-10-25
배경색상 #77CC00
  • Date :  2022-10-25 (Tue) 10:00 ~ 12:00
  • Place :   Zoom
  • Speaker :  Travis Scrimshaw (Hokkaido University)
  • Titles & Abstracts :

I.   Rational liftings and gRSK  (10:00 ~ 11:00)

Kashiwara's theory of crystal bases has been fruitful to many different areas of mathematics. A classical application has been to representation theory (where it originates), which leads to another combinatorial proof of the Cauchy identity, where the famous Robinson-Schensted-Knuth (RSK) bijection becomes an isomorphism of crystals. However, its discrete (and combinatorial) nature makes it hard to work with sometimes, so we transform its description into piecewise-linear functions. This description allows us to construct a rational lifting, enabling a more continuous theory of crystals that can lead to further connections. This was formalized in the work of Berestein and Kazhdan with their theory of geometric and unipotent crystals. The RSK bijection can also be formulated into piecewise-linear functions, which has a rational lifting to an isomorphism of algebraic varieties called geometric RSK (gRSK) with nice properties. In this talk, we discuss the background on geometric crystals and gRSK, including the two different descriptions due to Noumi-Yamada and O'Connell-Seppäläinen-Zygouras.

 

II.  Crystal Invariant Theory  (11:00 ~ 12:00)

In this talk, we show that gRSK is a (A_n x A_k)-geometric crystal isormohpism, providing a rational lifting of the now classical result about RSK. We will then discuss applications to the field of invariants under the various geometric crystal operators and the geometric R-matrix. This is based on joint work with Ben Brubaker, Gabriel Frieden, Pavlo Pylyavskyy; arXiv:2112.00524, arXiv:2205.12681.

 

 


List of Articles
번호 제목 글쓴이 날짜 조회 수
공지 QSMS Mailing List Registration qsms 2021.09.09 33975
72 [QSMS Seminar 20220721] Finding ALL solutions qsms 2022.07.14 15589
71 [SNU Number Theory Seminar 2022-06-21] Arithmetic local systems over the moduli space of curves qsms 2022.07.21 15421
70 [SNU Number Theory Seminar 2022-08-08] Geometry of the $B_{dR}^+$-Grassmannian qsms 2022.08.04 15448
69 [SNU Number Theory Seminar 2022-08-11] The dual Lagrangian fibration of hyper-Kähler manifolds qsms 2022.08.04 15994
68 [QSMS Seminar 2022-08-24] Vector bundles and representation theory on a curve qsms 2022.08.13 15526
67 [QSMS Seminar 2022-08-31] Localization of the category of modules over quiver Hecke algebras qsms 2022.08.25 15545
66 [QSMS-BK21 Seminar] Past seminars qsms 2022.08.26 15394
65 [QSMS-BK21 Seminar 2022-08-29] Symplectic Cohomology, String Topology, and Deformations qsms 2022.08.29 16453
64 [SNU Number Theory Seminar 2022-09-16] Height-moduli and lower order terms qsms 2022.09.06 16138
63 [QSMS Seminar 2022-10-11] (q,t)-Cartan matrix and representation theories related to the specializations of the matrix file qsms 2022.09.18 17264
62 [QSMS Seminar 2022-09-27] Categories of Whittaker Modules over Lie superalgebras and Categorification of Fock Spaces qsms 2022.09.20 17205
61 [QSMS-BK21 Symplectic Geometry Seminar 2022-09-30] Introduction to Floer Homotopy: Bordism and Flow Categories qsms 2022.09.26 17725
60 [QSMS Monthly Seminar 2022-09-30] Monotone Lagrangians via toric degenerations: algebraic approach qsms 2022.09.30 15616
» [QSMS Seminar 2022-10-25] Rational liftings and gRSK qsms 2022.10.08 14680
58 [SNU Number Theory Seminar 2022-11-11] Mixed moments and the joint distribution of random groups qsms 2022.10.24 15673
57 [QSMS-BK21 Symplectic Geometry Seminar 2022-11-04] Introduction to Floer Homotopy: Kuranishi Structures qsms 2022.10.26 16039
56 [SNU Number Theory Seminar 2022-11-04] Approximations with mod 2 congruence conditions qsms 2022.10.27 15581
55 [QSMS Monthly Seminar 2022-10-28] Oscillator representations of quantum affine algebras   qsms 2022.10.30 15288
54 [QSMS Seminar 2022-12-2] N=2 supersymmetric W algebras from Hamiltonian reduction qsms 2022.11.25 14315
53 [QSMS-BK21 Symplectic Geometry Seminar 2022-12-09] Introduction to Floer Homotopy: Formal Groups and Complex Cobordism qsms 2022.11.28 15968
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8