May 2025 - Cart-seminar - snurep.crystalline.site

(Reminder) CART Seminar announcement (Daniel Bump, May 23 (Fri), 9:00AM)
by 이신명 21 May '25

21 May '25

Dear all, This is a gentle reminder of the CART seminar by Daniel Bump (Stanford University) on 9:00 - 10:00 am tomorrow (in Korea time). Hope to see you at the seminar! Best regards, Sin-Myung Lee -----------------------원본 메세지----------------------- 보낸사람: "이신명"<sinmyunglee(a)kias.re.kr> 받는사람: "All Members(all)" <all(a)kias.re.kr>, cart-seminar(a)snurep.crystalline.site 보낸날짜: 2025-05-16 01:45:39 GMT +0900 (Asia/Seoul)제목: CART Seminar announcement (Daniel Bump, May 23 (Fri), 9:00AM) Dear all, The upcoming CART seminar is scheduled for May 23rd (Fri), 9:00 - 10:00 (Korea time). Speaker: Daniel Bump (Stanford University, USA) Title: Solvable Lattice Models and Yang-Baxter Groupoids Abstract: We will review some applications of the Yang-Baxter equation to proving that certain partition functions represent functions of interest to combinatorialists such as Schur polynomials, Hall-Littlewood polynomials or Schubert polynomials. The underlying mechanism is the parametrized Yang-Baxter equation. Typically these are regarded as coming from quantum groups, and we will see how for the six-vertex model there is a contrast between the "free-fermionic" case relying on the quantum group U_q(sl(1|1)) and the non-free-fermionic case relying on U_q(sl(2)). A deeper look at the non-free-fermionic case leads to Naprienko's six-vertex groupoid. We will argue that groupoid parametrized Yang-Baxter equations may be common, and give another example of a groupoid parametrized Yang-Baxter equation in the five-vertex model. This talk will rely on joint work with Brubaker, Buciumas and Gustafsson, and with Naprienko. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/82269442887?pwd=7DdbmNqDVY1SIjfoNzXBP3XBGarK5V.1 Meeting ID: 822 6944 2887 Password: 294582 Please feel free to forward this to anyone who might be interested. You can check out further information on CART seminar on our website (https://sites.google.com/view/cart-kias/). Looking forward to seeing you at the seminar! Best regards, Sin-Myung Lee

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CART Seminar announcement (Daniel Bump, May 23 (Fri), 9:00AM)
by 이신명 16 May '25

16 May '25

Dear all, The upcoming CART seminar is scheduled for May 23rd (Fri), 9:00 - 10:00 (Korea time). Speaker: Daniel Bump (Stanford University, USA) Title: Solvable Lattice Models and Yang-Baxter Groupoids Abstract: We will review some applications of the Yang-Baxter equation to proving that certain partition functions represent functions of interest to combinatorialists such as Schur polynomials, Hall-Littlewood polynomials or Schubert polynomials. The underlying mechanism is the parametrized Yang-Baxter equation. Typically these are regarded as coming from quantum groups, and we will see how for the six-vertex model there is a contrast between the "free-fermionic" case relying on the quantum group U_q(sl(1|1)) and the non-free-fermionic case relying on U_q(sl(2)). A deeper look at the non-free-fermionic case leads to Naprienko's six-vertex groupoid. We will argue that groupoid parametrized Yang-Baxter equations may be common, and give another example of a groupoid parametrized Yang-Baxter equation in the five-vertex model. This talk will rely on joint work with Brubaker, Buciumas and Gustafsson, and with Naprienko. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/82269442887?pwd=7DdbmNqDVY1SIjfoNzXBP3XBGarK5V.1 Meeting ID: 822 6944 2887 Password: 294582 Please feel free to forward this to anyone who might be interested. You can check out further information on CART seminar on our website (https://sites.google.com/view/cart-kias/). Looking forward to seeing you at the seminar! Best regards, Sin-Myung Lee

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CART Seminar announcement (Soo-Hong Lee, May 2 (Fri), 10:30AM)
by 오재성 01 May '25

01 May '25

Dear all, The upcoming CART seminar is scheduled for May 2nd (Friday), 10:30 - 11:30 (Korea time). Speaker: Soo-Hong Lee (Seoul National University, Korea) Title: Infinite level Fock space, crystal bases, and tensor products of extremal weight modules of type A_+∞ Abstract: We construct an infinite-level Fock space that admits commuting actions of the quantized enveloping algebra of infinite affine type A_+∞ and the parabolic boson algebra associated with (gl_∞, gl_{∞\0}). This construction extends the classical Howe duality on higher-level Fock spaces. Its study revisits a subtle phenomenon in which the crystal base of a proper submodule coincides with that of the entire space — a behavior previously observed in level-zero representations of affine type by Kashiwara, Beck, and Nakajima. In the A+∞ type, we show that this combinatorial phenomenon is intricately tied to the socle filtration of ambient representations. Utilizing this connection, we construct a saturated crystal base through a limiting process and provide a comprehensive description of the socle filtration for extremal weight modules of type A+∞, recovering coefficients first obtained by Penkov and Styrkas. This is a joint work with Jae-Hoon Kwon. You can join the seminar via the following Zoom link: https://us06web.zoom.us/j/85728812852?pwd=mYaLjZSh5ZaPbNmXbExIuthHU4vFiW.1 Meeting ID: 857 2881 2852 Password: 537826 Please feel free to forward this to anyone who might be interested. You can check out further information on CART seminar on our website (https://sites.google.com/view/cart-kias/). Looking forward to seeing you at the seminar! Best regards, Jaeseong Oh

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