http://www.stat.ucla.edu/~ywu/mirror.pdf Web19. mar 2012 · We prove that the stable parts of the parabolic Hitchin complexes for Langlands dual group are naturally isomorphic after passing to the associated graded of the perverse filtration. Moreover, this isomorphism intertwines the global Springer action on one hand and Chern class action on the other.
RELATIVE LANGLANDS Slogan: the relative Langlands program …
Web6. feb 2024 · Given a compact connected Riemann surface X equipped with an anti-holomorphic involution and a complex semisimple Lie group G equipped with a real structure, we define anti-holomorphic involutions on the moduli space of G-Higgs bundles over X. We describe how the various components of the fixed point locus match up, as … Web26. aug 2024 · Let X denote a projective variety over an algebraically closed field on which a linear algebraic group acts with finitely many orbits. Then, a conjecture of Soergel and Lunts in the setting of Koszul duality and Langlands' philosophy, postulates that the equivariant derived category of bounded complexes with constructible equivariant cohomology … fz3-700
SPHERICAL VARIETIES, L-FUNCTIONS, AND CRYSTAL BASES
Web4. nov 2024 · According to the Langlands functoriality conjecture, broadened to the setting of spherical varieties (of which reductive groups are special cases), a map between L … Webconnects these dualities in more general and modern ways from various areas of mathematics. In the classical Langlands program, the correspondence between elliptic curves and automorphic forms are all about the correspondence between the eigenvalues of Frobenius operator and Hecke operator. 4 WebThe point is that spherical varieties have good combinatorics: they have now been classi ed (over C) in a way analogous to the classi cation of split reductive groups via root datum. … fz2999