Konferenz: Swiss-Russian Seminar on Moduli Spaces and Physics


On the center of the small quantum group

{{_Ltalk:R}} A. Lachowska
Datum: 06.12.07   Zeit: 09.00 - 10.00   Raum: Y27H36

Abstract: The small quantum group $u_l$, as introduced by Lusztig, is a quotient of the quantum enveloping algebra of a semisimple Lie algebra $g$, with the quantization parameter specialized to an $l$-th root of unity. Its structure and representation theory is related to various fields of mathematics, such as the representation theory over the fields of positive characteristic, and topological invariants of $3$-manifolds. The structure of the center of $u_l$ is a long known difficult problem. I will present a description of the center of $u_l$ in terms of cohomologies of certain coherent sheaves on the flag variety $G/B$ corresponding to the Lie algebra $g$, and discuss several examples. This is a joint work with R. Bezrukavnikov.