Mirror symmetry in the character table of SL_n(F_q) - GEOM - EPFL
Mirror symmetry in the character table of SL_n(F_q) - GEOM - EPFL
Mirror symmetry in the character table of SL_n(F_q) - GEOM - EPFL
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Cartoon II<br />
(Strom<strong>in</strong>ger–Yau–Zaslow 1996) mirror <strong>symmetry</strong> for<br />
MDol(G)<br />
MDol(G<br />
<br />
<br />
χG <br />
<br />
L )<br />
χGL <br />
A<br />
(Hausel–Thaddeus 2003; Donagi–Pantev 2006 )<br />
⇓<br />
Homological mirror <strong>symmetry</strong> = Geometric Langlands<br />
D b (Coh(MDR(G))) ∼ D b (Fuk(MDR(G L )))<br />
(Kontsevich 1994; Laumon 1987)<br />
(Beil<strong>in</strong>son–Dr<strong>in</strong>feld 1995; Kapust<strong>in</strong>–Witten 2007)<br />
⇓<br />
semi-classical limit fiberwise Fourier-Mukai transform<br />
D b (Coh(MDol(G))) ∼ D b (Coh(MDol(G L )))<br />
(Ar<strong>in</strong>k<strong>in</strong> 2002, Donagi–Pantev 2009)<br />
⇓<br />
4 / 15
Change language