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