Views 3378 Votes 0 Comment 0
?

Shortcut

PrevPrev Article

NextNext Article

Larger Font Smaller Font Up Down Go comment Print
?

Shortcut

PrevPrev Article

NextNext Article

Larger Font Smaller Font Up Down Go comment Print
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
No. Subject Author Date Views
Notice QSMS Mailing List Registration qsms 2021.09.09 13291
150 [QSMS Seminar 2021.07.02] Lefschetz fibrations on cotangent bundles qsms 2021.06.29 47792
149 [초청강연 2020.11.27] Zeta함수와 L함수에 대한 역사적 고찰II qsms 2020.11.23 34968
148 [SNU Number Theory Seminiar] 2021.10.08 qsms 2021.08.23 24698
147 [QSMS Monthly Seminar] Peterson conjecture via Lagrangian correspondences and wonderful compactifications qsms 2020.11.18 23302
146 [Seminar 05.14, 05.21, 05.28, 06.04] Introduction to derived categories qsms 2021.04.16 19566
145 [Seminar 2021.03.03] Zeta함수와 L함수에 대한 역사적 고찰X qsms 2021.03.02 12019
144 [Seminar 2021.04.02] Quantum affine analog of Kazhdan-Lusztig positivity for non-simply laced types via simply laced types qsms 2021.03.30 10864
143 [QSMS Monthly Seminar] Canonical basis qsms 2020.11.18 9585
142 [QSMS Monthly Seminar] Introduction to cluster algebras (and monoidal categorification) qsms 2020.11.18 9156
141 [Seminar 2021.04.16] Hecke system of harmonic Maass functions and applications to modular curves of higher genera qsms 2021.04.19 8602
140 [2021 KMS Spring Meeting] Related talks qsms 2021.04.30 7770
139 [초청강연 2020.11.20] Zeta함수와 L함수에 대한 역사적 고찰 qsms 2020.11.18 6674
138 [Seminar 2021.04.29] A realization of type A finite $W$-(super)algebra in terms of (super) Yangian qsms 2021.04.09 5428
137 [Seminar 2020.12.03~05]Visual Studio Code를 사용하여 편리한 LaTeX 환경 구축하기 qsms 2020.12.02 5032
136 [Seminar 2021.04.02] CM congruence and the derivatives of p-adic L-functions for imaginary quadratic fields qsms 2021.04.19 4912
135 [Seminar 2020.11.25] On the ordering of the Markov numbers (AM 10:00~12:00) qsms 2020.11.18 4875
134 [정수론 집중강연 2021.08.03, 08.05] Geometric approaches to the local Langlands correspondence I-IV qsms 2021.07.29 4830
133 [Seminar 2021.06.15, 06.22] Cluster algebras with a view toward the Jacobian conjecture qsms 2021.05.28 4808
132 [Seminar 2021.05.28] Ramanujan continued fractions of order sixteen qsms 2021.05.21 4735
131 [Seminar 2021.04.23] Quiver Hecke algebras and unipotent quantum coordinate ring qsms 2021.04.09 4692
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8