Characteristic Cycles and Semi-canonical Basis
Time: Thu, 4 Jul 2019, 13:30-15:05
Place: First conference room at Jinchunyuan West Building (近春园西楼)
Speaker: Taiwang Deng (Max Planck institute for mathematics)
Abstract:
Twenty years ago Lusztig introduced the semi-canonical basis for the enveloping algebra U(𝖓), where 𝖓 is a maximal unipotent sub-Lie algebra of some simple Lie algebra of type A, D, E. Later on B. Leclerc found a counter-example to some conjecture of Bernstein-Zelevinsky and related it to the difference between dual canonical basis and dual semi-canonical basis. He further introduced a condition (open orbit conjecture of Geiss-Leclerc-Schoer) under which dual canonical basis and dual semi-canonical basis coincide. In this talk we explain in detail the above relations and show a relation between the two bases above through micro-local analysis.