Seminar Event Detail

RTG Representation Theory

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. Files: Speaker:  Calvin Yost-Wolff Institution:  UM Event Organizer:

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