|Date: Monday, September 27, 2021
Location: 4088 East Hall (4:00 PM to 5:15 PM)
Title: Borel--Weil--Bott over C
Abstract: The Borel-Weil-Bott theorem describes the cohomology of line bundles on flag varieties as certain representations. In particular, the Borel-Weil-Bott theorem gives a geometric construction of the finite dimensional irreducible representations for reductive groups. In this talk, I will explicitly compute these representations for SL2(C). I will then motivate our previous computations with induced representations and Serre duality, leading to the Borel-Weil-Bott theorem for SL2(C). Lastly, I will use the Atiyah-Bott fixed point formula to deduce the Weyl character formula from our geometric representations.
Speaker: Calvin Yost-Wolff